I do not consider myself an artist when playing a game. I'm not expressing anything. Just trying to win. Would also not consider athletes artists, generally speaking.
If you’ve not mastered a play style than I wouldn’t call you an artist either.
I’ll use Martial Arts to prove my point. The word Arts is in the name. In martial arts you first have to master the basic movements of the particular school you're studying, just like pianists have to master moving their fingers in special ways to play cords and scales, and painters have to master shadowing and perspective.
Once you master the basic skills of your chosen art, then you can become more creative and do things freely while still staying true to the foundation. At this point I would consider one an 'artist.'
The word art in martial arts is being used in a different sense than it is in the op which refers specifically to a piece of art. Art can refer to a particular skill or study (i.e. Arts and Crafts, Martial Arts, Industrial Arts, Liberal Arts) but that's not what we typically mean when we refer to "pieces of art". If you want to use the term art to refer to anything that fits under any definition of art, then fine, playing games is an art, I'm not going to argue semantics. However, when we talk about art in the sense of pieces of art, we typically are referring to something that is intentionally expressive or evocative.
A guitarist composing or performing a piece is an expressive act, in most circumstances. A player playing Guitar Hero, no matter how skilled, is not really engaged in any type of expressive act. The only message being conveyed is "this is the most effective way to hit the buttons being demanded of me". To the extent creativity is employed, it is not done to express any particular message or feeling, just based on efficiency. There may be some scenarios where playing a game could be expressive, but by and large, it is not.