I found a fairly recent redo of the "classic" mental rotation by Foroughi et al (2015) which also reproduced the "classic" results (unlike the study in my question):
Many studies have found gender differences in mental rotation ability in young adults when completing mental rotation tests on paper and pencil (e.g., Peters et al., 1995; Vandenberg & Kuse, 1978). Two previous studies have been unable to replicate these findings when testing mental rotation ability inside of a virtual environment (Parsons et al., 2004; Rizzo et al., 2001). We created a new virtual mental rotation test (VMRT) based on a full, validated test of mental rotation ability (MRT-A; Peters et al., 1995) that 128 participants (79 females) completed while wearing an Oculus Rift DK1. Our data replicate previous findings of paper and pencil tests of mental rotation ability: men scored approximately one standard deviation higher (d = .90) than women.
It's worth noting that the study of Parsons (and also Rizzo, which I didn't know about) both used ImmersaDesk 3D, but more importantly they differed in methodology from "classics" (pen-and-paper) in that in Parsons' or Rizzo's version wasn't a multiple-choice test, but just a speed of rotation test:
Additionally, in both studies, a base stimuli
was presented and then replaced with a working
stimuli. The dependent variable in these studies was
the time it took to successfully rotate the working
stimuli to correctly match the base stimuli.
However, most of the traditional mental rotation
tasks showing the gender effect use a comparison based
test where a base stimuli is presented
simultaneously with multiple working stimuli that
may or may not match the base stimuli.(e.g., Peters
et al., 1995; Vandenberg & Kuse, 1978). In these
studies, participants must then identify which
stimuli are correct (i.e., accuracy).
After stating their result is in contrast to Parsons' they comment/repeat that
there are many possible reasons for the differences in results. First, we replicated a full, validated test of mental rotation (i.e., MRT-A). Additionally, we scored our test for accuracy whereas Rizzo and
colleagues (2001) and Parsons and colleagues (2004) measured the time to rotate a working stimulus to match a base stimuli. Second, we used a
newer technology (i.e., Oculus Rift DK1) that may
have had a higher quality or fidelity facilitating
performance on the test. Third, the generation of
participants in our study may be more familiar with
technology (e.g., smart phones, tablets, etc.) as a
whole now that technologies are ubiquitous.
Future research should be directed at
determining whether scores on the VMRT are
predictive of performance on tasks inside of VE,
namely tasks tapping spatial ability. For example,
studies have shown new surgeons benefit from
simulated VE training (e.g., Seymour, 2008;
Seymour et al., 2002). Visuospatial skills are
necessary to successfully interact and complete such
tasks; thus, it would be interesting to determine
whether scores on the VMRT predict performance
on a simulated surgery task.
In other words, they reproduced the classic result by more faithfully sticking to the classic paradigm (multiple choice answer) in the virtual version. But it's also not clear how this impacts spatial skills the more usual ways they are used in a virtual environment.