Of course they count. Re-releases also count in movies. Critics just don't vote for them, because they shouldn't win.
The only way that re-releases would win is if you don't value originality at all -- which, frankly, is a current sharp criticism of the mainstream gaming industry; highly stagnant, conservative, and reliant on classic methods. Take that concept to the extreme, and you get games being re-released with a resolution bump winning "best game of the year."
So, it can win. It's allowed to, just like updated versions of films can win best film of the year. It would make us look very, very silly if it won, however.