Abandon4093 said:
Let me get this right.
Liars - lie.
Cheaters - cheat.
Gamers - game.
So sluts must.... slut?
This.
Liar, Cheater and Gamer are all the direct noun form of the verb. "Slut" is not related (etymologically speaking) in any way to sex or sleeping with people - there is no pattern there, it has nothing in common with the other words. Sex doesnt even
have a verb sense like lie, cheat and game do - there is no such word as a "sexer".
At best, the line of reasoning in the OP could vaguely argue that a slut is somebody who "sluts". Again, that proves nothing about how it relates to sex.
If OP really wants a word that fits the pattern - try "copulator", or "fornicator". Both words that directly mean "somebody who has sex", and dont have additional insult or judgement attached.