A marriage between two people of the same gender who are not gay. Usually considered the pinnacle of a bromance where two bro's decide to become partners for life in a straight way. This is like in that movie "I Now Pronounce You Chuck & Larry." Although Chuch and Larry were pretending to be gay, they were actually two straight men who married for reasons involving pensions or something.
"Don't worry man, everyone here knows this is a non-gay gay marriage."