This term was derived off of a video game called Starcraft which had a tactic where you are able to rush opponents by mass producing zergs and rushing them
"All you pussies can do is Zerg Rush."
Originated from the game StarCraft, in which if timed correctly you could send a dozen zerglings (lowest-level soldier avalible) into the enemy's base before they could make defenses. Spread to include any battle tactic that involved massive amounts of zerglings to overwhelm the enemy's defense.
"Why bother wasting resources on Ultralisks when 4 dozen zerglings can rip a Protoss base up like tissue paper in a zerg rush?"
Protoss Player: Oh no, my precious zealots are too expensive for me to buy more than one. I'm screwed.
Terran Player: *Flys to higher ground* What a bunch of fags.
Originally started on the RTS game Starcraft due to the inexpensive Zergling unit being used in the manner described above.
Its not only used in SC, but other games and just a random computer thing to yell.
Player B: =D
Person A: ZERG RUSH LOL!