TLDR version: PVT or the Mackworth clock test seems to have been most successful in the category of computer-based testing that doesn't require specialized (e.g. pupillometry) equipment. Mackworth's seems to lack standardization though.
The two tests also belong to different sub-categories, which highlights a need to refine the notion of alertness. PVT only "discriminates" against single class stimuli, only their timing is uncertain, so it's a detection task; the corresponding notion it supposedly measures been dubbed “intrinsic alertness” or “psychomotor vigilance”. Mackworth's discriminates between two classes of stimuli (i.e. it belongs to a wider go/no-go class of tasks); this is the typical/classical paradigm for “vigilance” testing. Since 2004, the term "vigilant attention" has been proposed to encompass both detection and discrimination tasks; it has gained some traction in the literature. The proponents/adopters of this new term argue that "vigilance", "alertness", "sustained attention", and "arousal" are/were not terribly well defined.
Subjective alertness (easily measured on a paper-based [self]-test) doesn't seem a good predictor of PVT (Phillips et al., 2016).
The Mackworth clock test appears to be most sensitive based on Williamson and Feyer (2000):
This study shows that commonly experienced levels of sleep deprivation depressed performance to a level equivalent to that produced by alcohol intoxication of at least a BAC of 0.05%. At the end of periods of waking of 17–19 hours, performance levels were low enough to be accepted in many countries as incompatible with safe driving. The earliest effects were seen for the Mackworth clock test and the latest for the dual task, although there was relatively little variation across tests. Longer periods of sleep deprivation were equivalent to higher alcohol doses for all tests except the grammatical reasoning and memory and search tasks. [...]
As expected, increasing concentrations of alcohol produced significant reductions in performance for most tests and measures. [...] The results show that the extent of loss of function varies between tests although there were consistent effects within different types of measures. At a BAC of 0.05% for example, response speed decreased by around 8%–15% for reaction time, dual task, Mackworth vigilance, and symbol digit tests corresponding to a slowing of around 45, 66, 136, and 182 ms respectively. Hand-eye coordination measures showed a similar overall decrement of around 10% at this BAC. Measures of overall test accuracy also showed significant decrements due to alcohol, especially the number of missed signals in the reaction time test, which increased by 200%, and the number of false alarm responses in the Mackworth test, which were more than 50% higher at a BAC of 0.05%. The number of correct responses in the Mackworth test and length of the recalled series in the spatial memory task also both decreased by about 13% at a BAC of 0.05%. Subjective ratings of tiredness also showed a significant linear decrement of 77% by a BAC of 0.05%. Two tests, grammatical reasoning and memory and search tests showed very little decrease in performance at a BAC of 0.05%.
[Snip para about effect BAC of 0.1%].
These results show that alcohol does not exert universal effects on all functions and the pattern of effects also differs between them.
Sleep deprivation also produced decrements in both performance and self rated alertness. As shown in table 5, sleep deprivation showed effects on a similar range of tests as did alcohol. [...] performance decrements occurred with increasing sleep deprivation for both speed and accuracy measures of the reaction time, dual task, tracking, and Mackworth tests and for the length of the recalled series for the spatial memory test. For example, between around 1900 and 0500 (corresponding to about 13–23 h sleep deprivation), reaction speed decreased by 57% for the Mackworth test, 9% for reaction time, 27% for dual task and 15% for symbol digit tests. Hand-eye coordination decreased by between 31% for the tracking component of the dual task and 26% for the tracking task alone. Accuracy also decreased markedly with sleep deprivation. The number of missed signals increased by more than 40% for the Mackworth test, by 187% for the reaction time test, and the number of false alarms increased by 200% for the Mackworth test. The symbol digit test only showed decrements for the speed measures but not the accuracy measure. The grammatical reasoning and memory and search tasks showed only relatively small decreases of around 5%–10% with increasing sleep loss for any measures.
Wikipedia shows a screenshot of a computerized version of the Mackworth clock, with this description:
The Mackworth Clock is an experimental device used in the field of experimental psychology to study the effects of long term vigilance on the detection of signals. It was originally created by Norman Mackworth as an experimental simulation of long term monitoring by radar operators in the British Air Force during World War II.1 The device has a large black pointer in a large circular background like a clock. The pointer moves in short jumps like the second hand of an analog clock, approximately every second. At infrequent and irregular intervals, the hand makes a double jump, e.g. 12 times every 30 seconds. The task is to detect when the double jumps occur by pressing a button. Typically, Mackworth's participants would do this task for two hours. The Mackworth Clock was used to establish one of the fundamental findings in the vigilance and sustained attention literature: the vigilance decrement, that is, signal detection accuracy decreases notably after 30 minutes on task. The test continues to be used today in vigilance research in various forms, including computer-displayed versions.
What's missing from Williamson and Feyer is a more detailed description of their tests, including the length of Mackworth clock; since they measured it repeatedly, I suspect they took a lot less than two hours for each round.
In the press release you found, Optalert links to an earlier one claiming to be setting a (new) "gold standard" with their tech. But their tech requires eye-tracking goggles, so not quite fitting your simpler requirements. And it's far from being the only such product on the market, A 2014 review by Dawson et al. lists and evaluates (just based on publications, it's not head-to-head test) more than two dozen competitors for continuous monitoring and about half-dozen for spot fitness testing. For the latter category, which is closer to what you ask for, they give this summary:
I'll only quote you the part about PVT from the review because the next best candidate in that table (FIT) requires pupillometry:
The psychomotor vigilance test
assesses sustained attention and is currently the gold standard in
fatigue detection. Individuals give a button-press response to visual
stimuli on a computer screen over a 5- or 10-min period. Reaction
time and ‘lapses’ (response time >=500 ms) are measured. Several
commercial versions of the PVT are available (e.g., PalmPVT, http://www.corware.com/Default.aspx; PVT-192: Ambulatory Monitoring,
http://www.ambulatory-monitoring.com/pvt192.html). The PVT has
consistently and reliably detected performance decrements resulting
from sleep restriction, extended wakefulness or time-of-day effects
across numerous industries, including rail, aviation, mining, and
defence. Validation evidence is available for both the 5-min and
10-min versions. However, PVT performance may not
equate to poor driving performance, perhaps due to large individual
differences in driving performance. Thus the PVT may be better used
to predict fatigue-related driving incidents as part of a broader test
battery. This possibility may be explored further through research
comparing the PVT with driving performance. Cut-off scores that
predict impaired driving performance have also not been established.
Despite its promise, until ‘fail’ or ‘warning’ levels are established,
this device is unlikely to be useful for commercial drivers.
And if you're curios of conceptual comparison between PVT and Mackworth's, Douwel (2016) master thesis offers:
To examine how attention is influenced during monotonous tasks, several vigilance
tasks have been designed like the Psychomotor Vigilance Task (PVT; Lim & Dinges, 2008),
the Continous Performance Task (CPT; Rosvold, Mirsky, Sarason, Bransome, & Beck, 1956)
and the Mackworth Clock Test (Mackworth, 1948). Each task and its measures have their
shortcomings and limitations. The PVT involves the detection of an unwarned stimulus to
which participants have to respond as fast as possible. A limitation is that the response to the
same signal is used, so no distinction is made between critical and non-critical stimuli.
Therefore it measures only the readiness for speeded responding to unwarned stimulation
(Langner & Eickhoff, 2013). The CPT and Mackworth Clock test involve discrimination
between target stimuli and non-target stimuli. Both stimuli appear intermixed in a constant
sequential stream consisting of regular intervals at a fixed rate. Participants need to respond
to targets and withhold a response to non-targets over prolonged periods of time. In general, the stream consists of more non-targets than targets and only the targets occur infrequently
and unpredictable. What it measures is a person's sustained and selective attention. Like the
PVT, this can be derived from the speed of responses, but also from the number of detected
and missed targets and the number of discrimination errors made. A shortcoming is that most
visual discrimination tasks contain stimuli-events at a regular and high rate. This does not
quite resemble real working environments in which the event-rate is at a slower pace and
stimuli occur irregular. Another shortcoming is that performance on the task is retrospective
which does not serve the purpose of preventing accidents from happening.
Lichstein (2010) notes a lack of standardization for Mackworth's (virtually every paper till then used a different variant).
CPT (mentioned by Douwel) seems to have given rise mostly to ADHD tests, thus not necessarily tests of temporary fatigue but more of a long-term impairment. (There might be some variant for fatigue that I don't know about.) For a factor structure of one variant CPT (which seems to include both a long-term impairment factors and short-term vigilance) see Egeland and Kovalik-Gran (2008).
Finally, for a more detailed discussion of the received terminology in the field see Oken et al., 2006, e.g.
Alertness is another term that overlaps with arousal but more specifically includes some cognitive processing. Some researchers use the terms phasic and tonic alertness (Nebes and Brady, 1993; Posner and Petersen, 1990). Phasic alertness relates to the orienting response (Sokolov, 1963) and tonic alertness will be used synonymously to vigilance and sustained attention.