Go predates online gaming a few thousand years
HOWEVER, since we all want to encourage new players on OGS and we all want OGS to grow [citation needed]), and many new players are just starting with go but may be used to other online games conventions (especially in the west), I think it is best to reduce ambiguity since as said before, “gg” means different things in different communities. I always use either “Have a nice game” or “Have a good game” at the beginning, the full phrase, which has a clear meaning. Similarly I end with “Thank you for the game”.
I recommend avoiding “gg” at all because in many e-sports and gaming communities, “gg” is not really synonymous with “good game”, as it carries a lot of extra connotation. It is used as a “technical” term or a “specific” word itself, “gg”, different from its origin “good game”. Similar to how in go we use “eyes” as a technical term with a specific meaning. The term literally means “each of a pair of globular organs of sight in the head of humans and vertebrate animals”, or anything resembling that. But when speaking of eyes, we use it as a technical specific go term quite different from the literal meaning.
In particular in Age of Empires 2 (and many other similar competitive games as far as I know, but this is the one I do know ) you never see people typing “good game” or saying “good game” like this when playing, they always use “gg” during the game. And the way it works is: the player who is going to resign says “gg”, or “gg wp” right before resigning. The other player acknowledges this by also answering “gg”, meanwhile the player who said “gg” first will be resigning. Saying “gg” first and not resigning would be a serious breach of etiquette that I do not remember seeing at all, just like saying “ok well played, I resign” on chat, while still continuing the game without resigning.
Note that when speaking out loud on stream, people often read the phrase “gg wp” that as “gg [gee gee] well played”, not as “good game well played”, further emphasizing that “gg” really feels like a separate, indivisible new word with a different meaning than a literal “good game”, while “wp” works much more similar to the actual “well played” phrase, as a normal abreviation.
In fact it also works the other way around, abbreviating a normal “good game” (the English words) as “gg” sounds bad. For example when commenting about a previous AOE2 game, if instead of saying “Yeah that game by Viper was such a good game, I enjoyed watching it”, someone said “Yeah that game by Viper was such a gg, I enjoyed watching it”, the meaning I hear is totally different. The first one means the normal English meaning, but the second one sounds to me something like “yeah in that game, the situation was such that the only thing to do is resign [“throw the gg in chat”]”, which sounds strange and if intended, is a totally different meaning.
The point is: “gg” has a very specific meaning in other games, it is NOT just the same as “good game”. I recommend avoiding it, as the “gg” abbreviation is not something that go players have been using for hundreds of years, like say, the word “Atari”.