"straight edgedrinking game" is a humorous expression that implies that a certain event or series of events will not happen, or will happen with very little regularity.
It's equivalent to saying "that will never happen", "no chance". "not in a million years" or other idiomatic expressions.
Example 1:
Joe: Hey, let's drink every time Bush says something smart.
You: Sup? You still trying tohook up with what's-her-name?
Her: Naw man, I just found out she's dating some guy she met in college... #StraightGate
You: What?! No way - I totally thought she was a lesbian!!!