Like the term "donkey", it refers to a bad poker player. The zonkey, however, makes especially flashy poker moves or uses language to indicate they "know" the game when it is just a matter of time until they "zonk" away all their money with their poor play.
The term is based on the animal called a "zonkey", which is a cross between a zebra and a donkey.
That zonkey was just saying how bad everyone was playing, then pushed all in when he was drawing dead. What a zonk!