I think it’s just your choice of word “act”. Yes it appears as game playing to me.

I don’t think he “acts” noncommittal and disinterested he might actually be noncommittal disinterested (or might be busy). I don’t think “acting” busy or hard to get is the way to be though. One can’t find available partner by acting unavailable.

I wouldn’t pursue him or act desperate either, that’s why I suggested not even contact him but wait for him to contact me and ask me out. If he isn’t contacting her, how would she even “act” busy or mirror him? But if he contacts and asks her on a date, I’d demonstrate interest and enthusiastically offered available time.