How do I play him at his own game?

People who play games are insecure. they put walls up to see if others will care enough to try and break through. they want to be chased & pursued, and this sounds like him. he sounds like he needs validation from you to feel better about himself and comfort his insecurities. so when he ignores you and sees you trying to go after him again, he's getting what he wants "you comforting his insecurities & making him feel better about himself"

Just stop contacting him. Don't feed into his need to be validated. Don't comfort his insecurities. Let him understand that you're not there to cater to his fragile emotions. If you have to BEG someone to spend time with you, talk to you, have sex with you, be in a relationship with you, marry you, etc.. then you KNOW that this person clearly doesn't WANT to do any of those things on their own. Just stop trying to initiate contact with him.

That way, if HE WANTS to talk to you, he'll call you. It's not like he'll not call you because he's afraid you might not be interested in him & he's afraid of being rejected or seeming creepy. He's already seen you try and contact him so many times. He has no excuse. He should feel completely comfortable, and nothing should be holding him back from talking to you if that's what he wants to do. You've shown him your interest. Now it's time he shows you his. Or else, just leave.