I know this might be a stupid question, so let say am stupid. But also let's say what if one the games I played this year is steam early access can that be on my goty list?
ThatFrood says you can list anything at all, but personally, I wouldn't consider those to be finished games. For example, DOTA 2 is a 2013 game because it was officially given a full release this year.
You're both right, but yes, you can include early access games. Obviously, the desired order of things is to submit games that came out, officially, this year. But at the same time the nature of this means you can submit whatever you like, as the aggregate always bears out. Out of a total of 300+ lists, your inclusion of your cat as your favorite game of the year will have no real effect. I'd prefer your list be personal and meaningful to you. Even if it's a bunch of stupid bullshit.
Basically, what I'm saying is submit what you feel meant the most to you in 2013. Hell, I have Earthbound on my list.
Additionally, aside from manually, I really have no good way of policing you.