A person who
frequently (usually at least once per week) plays
video games.
If the person in question only ever plays one
video game, that does not make him/her a gamer.
The word 'gamer' is vague, because it could refer to people who play games as a sport or for a living. These are simply subdefinitions that may be applicable to certain people.
''Nate's been playing
Fallout 4 for months now, probably every day. He even got to
level 100. Somehow, he's still got time to play other games too.''
- ''Seriously? I didn't even know he's a gamer. Maybe
we should hang out sometime.''