As a rule, can one create a Stack Exchange site dedicated to a specific computer game?
This is not necessary. We have Arqade.com, where you can ask questions about any computer game.
So, if you created a proposal for a specific game on Area 51, it would be closed as a duplicate of Arqade.
So, the answer is no.
In general, Stack Exchange tries to build sites that last, for a broad userbase. A single computer game is likely to lose interest over time, leading to a "ghost town" - an old site where nobody goes anymore.
Adding to S.L. Barth's answer, in most scenarios a game-specific site wouldn't be needed, as most questions could easily be applicable on Arqade.
That doesn't meant there aren't any scenarios where a more specific-focused site could be helpful.
Let's say there were a site proposal covering a specific game or subject matter.
- Is there a strong, passionate community of experts which could carry an entire site?
- Would this site fracture an existing community of users from other related sites?
- Would the site continue to thrive years from now?
- Could the site survive if the covered games/programs/topics wane in popularity?
While there aren't many great examples of this, there are a few exceptions. Take the split between Ask Ubuntu and Unix/Linux a few years back.
In the end, the split made sense, as Ubuntu had a strong, passionate group of experts that didn't want to be grouped with a more generalized "Unix/Linux" site. 7 years later, the two sites now co‑exist as healthy, independent communities.
Games like Minecraft or Eve Online might have communities which could cover questions and topics that may not be the best fit for Arqade. Whether or not there is a strong desire for game‑specific sites is another matter entirely.