Tagging here on Gaming is problematic, it's the subject of frequent debates and rants, and nobody is really satisfied by the status quo. Our subject just doesn't fit very well into the simple and general tagging system common to all SE sites.
Instead of trying to get the square peg into a round hole just by hammering harder (with the occasional, desperate use of power tools and explosives), the better solution would be to add an organizational system that fits to the specific needs of our subject.
The fundamental organizational principle here are the games themselves, the vast majority of questions can be just tagged with one specific game, and it's an unambiguous and extremely useful categorization. But games are not first-class citizens here, tags are the main organizational principle.
I propose that the top-level "tags" tab is replaced by a "games" tab, while tags would still exist the main organizational unit would be a game. The games page could display a nice list of games with icons/cover art and e.g. sorting by release date or other game specific information like genre. This would also be an opportunity to put up referral links to buy the games like SO does with books on Amazon.
Tags would still exist, but each game would have a separate hierarchy of tags, avoiding our ugly hacks along the lines of diablo-3-wizard and similar tags. This would enable us to finally come up with game-specific tagging schemes that are actually useful without causing all kinds of other problems.
The tag wiki could become more of an organizational focus when we actually have subtags for a game that provide some structure to our questions. It could outline the basic structure of our tags for that game, making it easier for users to find stuff and documenting the game-specific tagging structure at the same time.
Now, this whole idea has probably no chance of being implemented this way. Maintaining a completely separate system for just one site adds a significant maintanance burden. But there might be some ways to at least fake some of this user experience without having to completely redo the tagging system. And with the Diablo 3 craze right now we're the 3rd largest SE site right now, so we might be on the way of getting big enough to justify some custom development in that area.