It's not a Targ. The targ was invented afterwards and looks nothing like this animal, nor it has any reason to.
By this logic, pugs aren't dogs because they don't look like German Shepherds.
The animal in III doesn't look like a targ, doesn't walk like a targ, doesn't quack like a targ. The only thing it has in common with a targ is that both appeared in Star Trek, and one of them only from TNG on.
If Kirk found it in the ship after the movie he probably barbecued it since there is no meat to eat in Vulcan.
Now, pugs? what pugs? and you talk about my logic?