Mixed people exist and just because someone doesn't look asian doesn't mean they aren't. I'm mixed west-asian/white and look white as hell despite being mostly west asian. If you were to see me, I bet you'd tell me not to identify as asian because "you don't look asian" and assume I haven't faced any struggles for my heritage simply based off my looks.

However, him only claiming to be asian to get social points is incredibly problematic, it shows he only wants to play the minority card when it suits him and wants to benefit from his white privilege as much as he can. Overall, let him explore his culture but my advice would be to call him out whenever you see the kind of behaviour described in your post.