I think having a multiple choice selection would be nice, as that will ensure that we can see what the options are before voting. otherwise it is possible that everybody votes for a unique game and every game will then have one vote.
Could do two rounds of voting, firat one is a format like this, open ended. Where people can put whatever. And then round two takes games from round one in a multiple choice list. This wouod allow people to google the games and look them up to see what interests them.