I met this guy at a party and we had kept making eye contact from across the room. He later asked me if I wanted to be his partner for beer pong and I said yes. We flirted while we played, he gave me compliments about how good I was and he said we "had chemistry" because we were playing so well together. We had talked to get to know each other and he had actually been listening to what I was saying, unlike most guys I meet at parties. So all of this gave me the idea that he had liked me, but at the end of the night when me and my friends were leaving, he just shook my hand. Was I completely wrong about him liking me? Why did he just give me a hand shake?

Don't read into his hand shake. Sounds like you both enjoyed the evening.
He might have thought, since you both had been drinking, that it wasn't the night to pursue you.
Some like to find out more about a person before asking for more time with them. He might inquire friends about you. Or, be giving you a chance to do the same.
Im not sure what you expected him to do that night. But it was nothing that couldn't be accomplished on a future encounter.
Understand, he could have been waiting for your response to his hand shake to go something like... "It was really nice to meet you. I had a lot of fun. We should get together sometime and hang out."
I would check to see if he is seeing someone. Or, if he had gotten out of a recent relationship.

It's possible that he didn't want to come on too strong by getting your contact information right away. But there can be so many other possibilities. But instead of worrying about what he's thinknig, take it for what it is. Don't let his handshake overshadow the fun time that you had.

Is there a chance that you will see him again?

You both had a great time, cherish those moments, but you both were just strangers and he was a friendly polite guy, but you still don't know each other. Maybe you'll meet again, maybe you won't, but don't dwell to long on why he acted as he did.