This is going to be a tough one, because I won't list anything that wasn't actually released in 2013. The majority of this year was me working through backlog ranging from original XBox games like Jet Set Radio Future, to GTA IV and the expansions, to earlier Saints Row games, and plenty of other old stuff. Didn't buy the new consoles, either.
I do not claim that these are the ten best games that came out this year by any means, I just ordered the ones I did play. Aside from a ton of older games I still need to go through, I'll be adding Saints Row IV, Tomb Raider, and GTA V to my "someday I'll get to it" list.
I usually do wordy explanations for everything since I hate just throwing games out there without at least trying to convey why I feel the way I do about them, but I'll be leaving a lot of that out this time. This just wasn't a year that really grabbed me as far as gaming goes since I was so caught up in old stuff.
Walking Dead S2E1 and Wolf Among Us E1 are not in contention, going to wait until next year when we have the full picture.