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I don't think that one would count. After all, those animals aren't so much as funny or odd as the fact that they're usually regular animals who happen to be running a shop somehow for some bizarre reason. For example, in Vinditcus, a M Morpg, there's some normal animals who apparently runs shops and the marketplace. They don't talk at all, and apparently nobody owns them, so it's just not some mysteriously absent shopkeeper who left their pet behind to run things for them.
although in some other games those regular looking animals also happen to talk too. *shrugs* there really should be a trope for Animal shopkeepers.
Just found some tropes that would somewhat apply to this: The Intellectual Animal, and the uplifted animal. The animal shopkeeper could be a sub-trope of both those tropes, don't you think? there's also the Civilized Animal for some of those animal shopkeepers.
Is there actually a trope where You basically have Animal Shopkeepers in what is otherwise a very human(oid) world? Those animals can be anthropomorphic, the regular talking animal variety, or just very normal animal that has the uncanny ability to run a shop all on their own without help from a human being.
This trope wouldn't count if they were in a world where everyone else were animals. Just when they're in a world where it would be considered a little unusual once you notice that about everyone else is human, and you get to wondering where those anthropomorphic animals came from. or the fact that apparently nobody else finds it odd that a normal-looking parrot or a cat is able to run a shop all on their own, with apparently no human owner in sight.