I'm not sure what 'Fan Night' is, but I can tell you why it isn't 'Fans' Night'.
It is because 'fan' is an adjective and we don't make adjectives plural.
It's like saying 'blue shoes'. (not 'blues shoes')
Or 'four-door car'. (not 'four-doors car')
Actually, I've just found this link:
It looks like the TV audience get to choose which games they want to see during Fan Night. So you can vote for the game you want to watch.