To borrow a definition from Andrei Konchalovsky, art is that which imparts feelings. If a game does that, it's art. Many "gamey" games don't, and this is perfectly fine.
Consider two games, Inside (a great art game) and Overwatch (a great "gamey" game). Inside is much less rich in terms of gameplay, but (in my subjective opinion) does much more with feelings. Overwatch, on the other hand, is enormously, ridiculously rich in terms of gameplay, but when you're actually playing it (as opposed to viewing the art), it's more of a dopamine binge.
All games impart feelings even Overwatch! A really common game design lens is essentially “how do we want this to make the player feel?”
There’s definitely a very common set of feelings you might miss or not see as intrinsic because most games are imparting them but that doesn’t remove them from existence.
Consider two games, Inside (a great art game) and Overwatch (a great "gamey" game). Inside is much less rich in terms of gameplay, but (in my subjective opinion) does much more with feelings. Overwatch, on the other hand, is enormously, ridiculously rich in terms of gameplay, but when you're actually playing it (as opposed to viewing the art), it's more of a dopamine binge.