Well, the old manual specifically called it a "prehistoric" bird, and his Marvel TFU profile a "dino-bird".
That and the fact that he hung out with the Dinobots in "Call of the Primitives" and was even referred to as a Dinobot in that ep (at least I think I remember that?) kind of made me lean towards him being a dino.
So archaeopterix made more sense than anything else to me.
And there are no birds with teeth. It's part of what makes a bird a bird and not a dino, along with the feathers and hollow bones. They don't have separate, individual teeth with enamel set into a soft substrate. Those birds with "teeth" you mention have a sharp serrated ridge just inside their mouth which is part of their beak.

It's all one piece with no enamel. While every individual serration could be considered a "tooth" in a loose sense, like in a chain saw, that's not what's meant when comparing dinos and birds.
But... I can totally see a winged snake type dragon there too.
I have no idea what exactly the folks at Toybox JP were thinking of when they first molded the thing. Only what Hasbro USA decided to call it when they sold it here. A prehistoric bird and a tail-less cat. Which somehow had two tails.
Maybe it was supposed to be a dragon. Or a bird. Or a dinosaur. Maybe the bottom is a lion or even a dog. I mean, the thing is weird looking and kibbly enough to be whatever you want it to be.
I'd be really interested to find out what TAKARA thinks it is. Seeing as how this reissue is the first time they are making and selling the mold. Anyone have a reissue and read Japanese?
All I know is that mine broke into like ten pieces in the early nineties. Then the bottom got thrown out and the top sold in a garage sale. With the engines broken out. (My little brother was rough on the TF's.)