Uh GOGgalor obviously.

https://youtu.be/OMs5-6haCZ4?t=48s

GOGybytes ^_^

See, I've never heard the term "troglodyte" used colloquially to mean anything other than "brute", and often an ill-tempered and/or antisocial and/or ugly one. While that might aptly describe some of the denizens of this community [ba-dum-tssh], it's not a very complimentary word, even in its modified form. (I'm aware that "out-of-date person" is one of the generally accepted meanings; I've just never personally heard it used that way. :) )
I think "GOGnard" serves this same intent very well, and is less slanderous, to boot -- though it would still apply more to the grizzled veterans of gaming (and, therefore, the Good Old Gamers who still remain from the early years of this site) than to GOG users in general.

If I had to pick from the to terms in the thread title, I'd chose GOGer (though, like SirPrimalform, I'd also spell it "GOGger" -- "GOGer" looks like it should be pronounced like "GoGurt").

GOGer is official, for example see this:

<i>We decided to do something extra for all the <span class="bold">GOGers</span> out there...</i>

Gogliiins :)

Inspired by Game Boy, Vault Boy, Vault Girl and X-Men: GOGboy, GOGgirl (or GOGirl), GOGman, GOGwoman, GOGmen

Gd eye for spotting that, i hvn't seen an official statement from GOG mentioning the term b4 this. Well, i guess this just shows i was right aftall. ;D

I vote for GOGermeisters

Goganators

GoGermeister, the booze for gamers!!!

"Even better than Jägermeister!"

You could always introduce a little culture -- "GOGame et GOGsieur" :-P

I think I'm pretty consistent in "GOG user" or "GOG customer" but maybe not.

Yeah, Google supports your theory too. :D Just search "goger site:gog.com" and compare it with "goglodyte site:gog.com".

Or Gozer.