This is a primary subject of study in game studies and ludology, which are domains of theory and research unto themselves. Moreover, the question as it pertains to games might be interesting to ask over on Arqade, though I can't guarantee it would be "on topic" enough for their community. You might find the following questions from Arqade interesting, as they hint at some general principles:
Problems I've seen mentioned in answers to these (to which I relate personally as a gamer) include:
- The ability to continue playing for a longer time than one can engage in other activities
- Costs of quitting freely and abruptly, such as loss of progress or satisfaction from proximal goals
- Proximity of goals in general, and immediacy of gratification
- Social involvement and its time sensitivity: teamwork requires coordination with friends' schedules
- Availability of games on a PC: even when I go to work, I inadvertently bring games with me!
Finally, the existence of consequent problems in general is an important part of what motivates the use of the negatively connoting word, "addiction". Practically anything can be done to excess of course, but drawing and playing sports may have higher thresholds of activity before they become counterproductive overall. At high levels of activity and skill, drawing and sports become marketable trade skills, and athletic activity generally promotes health. Gaming has less obvious benefits too (see for review Johnson, Jones, Scholes, & Carras, 2013), but popular culture and research literature are both still catching up with this, as well as to the revelation that many of the supposed problems with gaming aren't so bad after all (e.g., aggression; Ferguson, Garza, Jerabeck, Ramos, & Galindo, 2013). Therefore, I wouldn't read too much into popular (mis-)usage of "addiction" in this case. That's also not to say that true gaming addiction doesn't exist; I don't honestly know, but I've heard of cases that seemingly ought to justify application of addiction models to game obsessions, so it may just be a matter of time before the DSM takes note. (If it hasn't already; again, I don't know, and wish I had more time to look into it!)
Anyway, considering what makes games fun might lead to some insights as to why they produce fanatics. Whether video games really produce more than these other hobbies is an empirical question that I haven't seen answered yet, but my intuition suggests you're probably right to think they do, because video games appeal to people on very many levels. Again, you might have a hard time finding articles on game studies that don't address ways to appeal to people and reinforce participation. By virtue of being designed expressly to entertain us and reinforce participation, video games represent a culmination of creative efforts and marketing experiences that probably should supersede less modern forms of entertainment and hobbies with other focal purposes, at least to the extent that game designers are good at what they do. They've been getting better with the advent of affordable, portable, high-powered computers designed to optimize the user interface; the advent of education in programming and game design; and the economic prosperity of game designing and publishing companies. Drawing, sports, and board games are more often (but not always) tied to simpler mechanisms and traditional designs, so it may make sense if these pastimes haven't been keeping up with those that capitalize directly on modern trends in technological and educational progress.
Since there's enough literature out there on game studies to keep anyone busy, I'll only list a subset of specific ways that video games appeal to players that relate to psychological theories of motivation:
- Enjoyment is what intrinsic motivation is made of. Producing enjoyment is a primary purpose.
- Extrinsic motivation also arises from the structure of requirements games impose upon players seeking their more intrinsically desirable rewards (e.g., you have to beat a boss before you get to watch a FMV, or "grind" to a higher level before you can use a spectacular new ability or exciting game mechanism)
- Scalable difficulty improves users' ability to optimize challenge, which leads to the flow experience in gaming when challenge is tuned just so to an individual's "Goldilocks zone": not too high or low.
- Social interaction is facilitated by multiplayer games in a variety of ways.
- Cooperation satisfies the need for affiliation or relatedness, and promotes self-transcendence. Game objectives that require teamwork also play upon introjected motivation when a person plays to avoid the guilt of letting down a teammate. Social support has widely documented ramifications for well-being.
- Competition satisfies the need for power or competence when it goes well for a player or promotes skill acquisition and refinement.
- Both kinds may satisfy the need for achievement, especially when one can show off to others! The promise of approval or respect from others is another form of extrinsic motivation.
- Variety in general is the "spice of life" (Barrett, 2009; Kahn & Isen, 1993), and is readily available across the broad range of games.
- Investment in goals with long time frames may promote well-being and intrinsic motivation.
- My own research (Stauner, 2013) demonstrates a weak, predictive relationship between the average time frame of students' goals (longer-term goals being rated higher) and change in well-being over an academic quarter $(\beta=.09, t_{(267)}=2.61,p=.009)$, though this isn't necessarily a causal relationship.
- Manderlink and Harackiewicz (1984) also claim that setting long-term goals can "enhance subsequent intrinsic motivation relative to conditions involving proximal goals or no goals."
- Video games have surely been extending the time frames of their players' goals. In my own adolescence, I recall finding an RPG that required 60 hours to complete exceptional. Newer games—especially MMORPGs—have increasingly adopted an expand-and-patch strategy to keep new content flowing for years of (potentially endless!) goal pursuit. Blizzard Entertainment's World of Warcraft is a prime example of a game universe that's taken on a life of its own since its release in late 2004; I've "met" some players who have been around since then myself.
- Long-term involvement in any goal or activity increases its relevance to a person's sense of identity, and may thereby affect the sense that the goal or activity is meaningful and important (identified motivation).
- Behavioral economic principles like sunk costs and escalation of commitment also explain why people have a harder time stopping a longer-term habit.
- Neurological bases of habituation are also an ongoing area of research that longer-term involvement and routinization would naturally make increasingly relevant regardless of initial motives.
References
Barrett, L. F. (2009). Variety is the spice of life: A psychological construction approach to understanding variability in emotion. Cognition and Emotion, 23(7), 1284–1306. Available online, URL: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2835153/. Retrieved February 5, 2014.
Ferguson, C. J., Garza, A., Jerabeck, J., Ramos, R., & Galindo, M. (2013). Not worth the fuss after all? Cross-sectional and prospective data on violent video game influences on aggression, visuospatial cognition and mathematics ability in a sample of youth. Journal of Youth and Adolescence, 42(1), 109–122. Available online, URL: http://www.christopherjferguson.com/Not%20Worth%20the%20Fuss.pdf. Retrieved February 5, 2014.
Johnson, D., Jones, C., Scholes, L., & Colder Carras, M. (2013). Video games and wellbeing: A comprehensive review. Sydney: Young and Well Cooperative Research Centre. Available online, URL: http://www.youngandwellcrc.org.au/document/ea0e9511fce02b8be23990_07ef7fc4c7/Videogames_and_Wellbeing.pdf. Retrieved February 4, 2014.
Kahn, B. E., & Isen, A. M. (1993). The influence of positive affect on variety seeking among safe, enjoyable products. Journal of Consumer Research, 20(2), 257–270.
Manderlink, G., & Harackiewicz, J. M. (1984). Proximal versus distal goal setting and intrinsic motivation. Journal of Personality and Social Psychology, 47(4), 918–928.
Stauner, N. (2013). Personal goal attainment, psychological well-being change, and meaning in life. (Doctoral dissertation, University of California, Riverside). Available online, URL: http://escholarship.org/uc/item/3t34c68w.
