Those long fins are really easy to break, and they grow pretty quickly. I would say that the other gourami did it... I don't know how well two male gouramis will do in a tank of that size, I had 2 blues in a 55 and they fought constantly and eventually had to be separated. Granted, blues get a great deal bigger than the dwarf varieties, but 29 gallons might be pushing it a little even for small fish. Bear in mind that gouramis and bettas are part of the same family of fish, and males will always fight one another (and females will fight with males as well, but not quite so fiercely with each other).
If it looks like one or the other is getting really beat up, I would suggest either finding a new home for it or transferring it to another tank.