I think your answer about genres and the idea of a tag set for sports is the best solution for this issue. The suggestion by alexanderpas of sports for titles that are collections of sports is probably the best use of that tag.
There are a number of sports games that identify the sport in the title, and the ones that don't really aren't that different than, say, WoW or CoD or SC2: if you aren't familiar with the title, you probably either aren't looking for content about it (to ask or to answer) or are looking for the specific game rather than the genre.
I also think there are few questions about a sports game that can really be applied to any sports game. I suppose there are probably questions about rules of or strategies within a particular sport (that could be better answered in a Sports.SE if one existed) that might need hockey or american-football, but even then, there simply aren't that many different titles within a particular sport, and how those rules and strategies are applied might well be specific to one title or one series, and are probably better tagged as the specific title that was being played when the question came up.
For example, someone might ask "What is the two-minute warning and what does it mean?" That's an American Football rule, but only in NFL football, so it wouldn't apply to EA's Arena Football or NCAA Football, and thus american-football doesn't apply. Rules also change in NBA basketball games at the two-minute mark, but those changes occur in each quarter rather than each half and are not the same as the NFL changes, so even sports would be misleading.
Tagging those questions with the specific title, like madden-10, also resolves issues with real-world rule changes that are reflected in subsequent titles. A question like "Why am I kicking off from the 35?" will have a different answer in Madden 12 due to the changes for the 2011 season; tagging it with american-football or even american-football-professional would lead to two different sets of correct answers (or three, depending on the depth of the question, to cover the earlier Madden games where kickoffs also were done from the 35 but other rules were different).