A person who plays one or more of the game applications on Facebook. Usually these people become very annoying with their constant game posts about what they need for their Farm, Fish, Mafia, Pets, etc. Such players also tend to spam inboxes with game invites and so called "free gifts".
Joe: "Man, Kate is really annoying me with all her posts. I can't see the important posts on my wall anymore because of her. She has really become a Facegamer"
Kevin: "After being laid-off for a few months, I really became a Facegamer and it kind of sucked to go back to work"
A person who plays Facebook games and considers themselves a real gamer.
Tony thinks he knows RPGs because he plays Mafia Wars. What a facegamer!
A particularly annoying kind of Facebook denizen who, knowingly or not, posts their idiotic game scores, ad nauseam, so that you have to scroll down reams of posts to see anything other than chickenshit in Farmville, or the like, even though these are supposed to be the people you're interested in hearing from. A facegamer is typically an old friend, now unemployed or underemployed, and may or may not be surprised to learn that their colossal waste of their own time is also wasting yours.
I used to like Brad, but he's become a loser, a facegamer for sure.