While related to concepts like "grammar nazi", by contrast a "grammerfuck" is not just someone who is strict about spelling and grammar, but someone who actively uses this tactic to attack someone they disagree with, to avoid direct discussion, or to undermine a debate.
The spelling of "grammar" as "grammer" in the word is intentional, to demonstrate how much you don't give a fuck about their rhetorical attack.
"You're family is rich, so I think you've got a different perspective on poverty."
"I think you mean 'your'. Maybe you should ask for your college tuition back?"
"Hey, don't be a grammerfuck, how about making an actual point?"