As in "some one who plays video games". Could I just use ゲーマー?
As rintaun says, ゲーマー is the most general term for "some one who plays video games".
In its narrower sense, when describing a person, it can mean a "hardcore gamer" as opposed to just ゲーム好き (げーむずき, casual gamer). For example, if someone wants to say she's just a casual gamer, she might say things like
If you need to differentiate between different gamer types, there are terms that roughly corresponds to the english ones.
- ライトゲーマー: casual gamer
- ミドルゲーマー: mid-core gamer
- ヘビーゲーマー: hardcore gamer
- コアゲーマー: especially avid fans among mid-core gamers
That's correct. ゲーマー is the word that is generally used.