Grammar gamer means a gamer who usually corrects your typos as a joke, They usually use laptops and play free games on steam. They also are bad at spelling so they use Grammarly or another app to correct their shittygrammar.
Fan of grammar. It's their name so capitalize it. That's their not there. I would start it with "and" ,but that's incorrect. That I needs to be capitalized by the way. Btw is incorrect.
You: lol look at that grammar fan.
Grammar Fan: Laugh out loud. Look at that grammar fan! (That's exclamative.)