I just spent, I don't know, an hour+ looking through articles concerning GameLit and LitRPG.
GameLit is definitely the newer term, and seems to have been developed so that it would include gaming derivative literature which didn't fall into the narrow definition of LitRPG; sunkuwan does seem to have a good grasp of what the accepted definition in the outer world is. And, based upon the gist of the various articles I read, he's correct in his predictions of how potential readers of the respective genres would react to a non-standard usage of the terminology.
LitRPG itself seems to divide into two main groups, but rather than the hard-SF/Soft-SF split, thye use the terms "crunchy" and "creamy", as in peanut butter; "crunchy" focuses on "number-crunching", it's heavy overt stat display, while "creamy" relies more on narrative to inform you of skills increasing. But in both cases, it does seem to require that you are involved with a MMORPG-like setting, predominantly or entirely within the game itself, and the game mechanics form a central part of the story.
So, yes, GameLit would be a more appropriate term for use here at SOL, as most of what shows up here doesn't really fit into the LitRPG sub-genre of GameLit.
I've read a number of works over the years which would be includable in the GameLit definition, but very few, if any, that would fall under the LitRPG def.
Even the one I just finished, over at BigCloset TopShelf, Morpheus' A Piece in the Game of Gods, and his earlier Kombat Champion, wouldn't qualify for LitRPG, for while very heavy on game mechanics, they are set in the Real World utilizing game machanics.
In both cases the MC is transformed into a real world version of a game character; the game mechanics function in the Real World as if it were actually a game. Which is almost the complete opposite of LitRPG.
It's a large enough community out there that using the terminology they've developed, now that we are aware of it, really would be the appropriate thing to do.
This does point out that, in the future, we may need to take a little bit more time and do a bit more research before bringing in new tags, just to make sure our understanding matches that of the community the tag is aimed at.
I wouldn't have been any use in determining what the proper tag should be, prior to doing the research I just did, since I had only recently discovered the lable LitRPG, and didn't know what, precisely, it covered, and was totally unfamilier with the term GameLit.