Public Display (Score 1)

As a law student who recently had copyright class, I think at least you have a decent shot at a fair use defense and its highly doubtful if you aren't commercial in nature, (ie: charging for the use of computers and licenses) that the companies would prosecute. If you want to be SUPER safe get the permissions. Think about the nature of the games, say Warcraft III, is by its nature amenable to use in Lan Party situations. Read the EULA for limitations, but would a company legitimately claim that the use of the "connect over lan" button they wrote really be a viable claim to a jury of a "public display?" So long as you aren't charging for the computers or to come in and watch and you all have licenses, then you should be just fine