The stress of it all may have caused him to bite his own fins. It happens with Bettas...they're rather sensitive to psychological stress. He's stop when his world has settled. But, if he doesn't, get some Blackwater Extract or Indian Almond Leaves in his water. They replicate the natural habitat and really ease anxiety in fish.
Did he suffer any injuries while with the Gourami at all? If so, there could have been reduced blood supply to some parts of the fins, and they died and fell off.
Fortunately, fins regenerate wonderfully well, and, with plenty of fresh, clean water and a bit of time, they'll grow back.
He's quite lovely-colored, by the way. At least, his dorsal fin is.