Even if we limited ourselves to game-specific subtags, there will be intersections between certain subtags that could reasonably apply to other games. Meaningful subdivisions within a game will not always be limited to things that are unique to that game. For example, there are a lot of questions on team-fortess-2 that are about how a specific weapon works, or how one weapon compares to another. It is helpful to be able to group this question about how a Team Fortress 2 weapon works with this question about how a Team Fortress 2 weapon works, which they otherwise have no identifying characteristics shared in their body text other than "Team Fortress 2".†
The game Lethal Crisis also has a very large selection of weapons, and weapon usage/unlocking/comparison could be a meaty subdivision for it. The thing is, the scope of the tag on both games is identical within the coverage of that game. They represent the same meaningful subcategory.
Having separate tf2-weapons and lc-weapons tags would get ugly pretty fast, and also very confusing. It'd be like differentiating zerg between starcraft and starcraft-2. Yes, they're the same alien species, but they are two separate games and the mechanics and identity of the Zerg between the two has changed. We don't do that because people grasp the logical connection of the tag to the appropriate game because the subdivision is identical between the games. I maintain that this is identical for weapon systems between Team Fortress 2 and Lethal Crisis. They may be completely different games, they may have entirely different mechanics to how weapons work, but the context and meaning of that tag for the question is the same. You could hot-swap the game names and the weapon names between questions in these two games and actually come out with legitimate questions.
Our most prominent problem in using subtags has been a lack of structure in identifying good subdivisions - a problem that spawns both disarray in their application, and also the creation of very poor subtags. Thanks to Skyrim moreso than anything, we're working on that. Whether they're game specific or not, sub tags will always pose the same problems. No, you can't really be a global expert on them. No, they can't exist as the sole tag on a question. They remain to create meaningful subdivisions, subdivisions that text search alone won't always be able to catch (see the above TF2 questions). If we are to use tags in this fashion, then, I believe that a more universal system, rather than a game-specific system, will provide greater benefit going forward.
In a game-specific system, we first have to address whether a game is popular enough to warrant subdividing. Then sometimes it's pretty easy (Minecraft and Starcraft were pretty easy), while other times like Skyrim you'll need to have discussions on what meaningful subdivisions exist. Then you'll need to make sure that you can create tags that are unique to be scoped just to the game but also unique to just the game, requiring prefixes or other approaches as necessary (say, if you can just limit it within a series). After we tag everything, we end up with a clean system that has good subdivisions. It is still limited only to the most popular games.
In a more universal system, we instead go in the reverse direction. We have a big discussion on what major subdivisions tend to be present (and I think Skyrim's system is actually strongly conducive to this for a general case). Then, we find the games where these subdivisions would be meaningful. We end up not limited just to the most popular, but are also able to catch games that, while spread out, don't quite hit the threshold. Moreover, this gives us an early-day advantage to help categorize questions with what we have - resolving then, yielding a need for other subdivisions, or even bowing down to more intuitive subdivisions like with Starcraft. We have a workable base that can be used to categorize questions while the content base is forming, rather than waiting on its creation to see what trends actually exist.
It's not without downfalls. It would require a lot of guidance and work and cooperation to come up with this set of base tags (a feat we've proven ourselves pretty poor at, most of the time). We'd also have to do a cleanup across the site afterwards, which while we do have a tiny question library compared to other big sites, we're still pretty hefty. However, I think that were we to take these efforts and apply them, the benefits and future time saved will be worth it.
...also, the likes of boss-fights needing to be split into individual games is quite irksome. Seeing as boss fights is such a wide-spread subdivision across FAQs and Walkthroughs for a plethora of games, it is a very expected division to expect in our Related Tags section or just in general. But if we limit ourselves only to game-specific subtags, we'd have to create horrid things like deus-ex-hr-bosses or zelda-bosses, which comes across very sloppy when you have the likes of zerg enjoying obvious associations.
†Focus more on the subdivision, not the literal text of weapons. As it were, I'm planning a separate post about fixes to that tag's name anyway.