What does Gg means

it depends on a game outcome.
If it was a draw - good game.
if you lost - giggle giggle.
if you won - goodbye goblin.

Of all of the meanings for GG given on the Wikipedia site below, Governor General was not listed.
GG is the Queen's representative in Canada. I suspect, however, the GG in question is Good Game and that is listed in the Wikipedia link.
https://en.wikipedia.org/wiki/GG

I think a lot of young gamers use GG to represent gratia gloriori, which in direct translation would be the joy of boasting, but a lot of these young guys and girls use it as a direct quote from the 5th century BC Roman consul Marcus Minucius Augurinus, who meant it much more as a rejoicing of collective achievement - hooray, aren't we all good!
At primary school my teacher said a GG meant a horse.
Maybe they think you play like a horse?