For one good reason that abbreviations in genres are dangerous, look at FPS. Miraculously, we have not actually run into any problem with it, but it's only a matter of time before the people asking about frames-per-second decide to lazy it up and tag it FPS. Which is sad, because both meaning of FPS are very critical in the gaming community.
Not to mention, some days I don't even know what the abbreviation stands for, even for my favorite genres like STG.
So for consistency's sake, I think we should think about moving over to expanded names. Once again, it's more clearly understood, and indeed it helps with searches. But unlike game titles, I don't think we need to clarify the acronyms as often in the post body. What a genre abbreviation stands for is understood by a much larger fraction of the gaming community, and for tagging we have auto-complete.
For MMORPG, see What tag should be used for MMO questions?