There is a German mad scientist, the dog is "a two-legged, four-armed genetically engineered robotic dog", whatever that meant in the 90s.

The Falconeer
Aerial dogfights with Warbirds, you can fight the "Kraken":
https://www.gog.com/game/the_falconeer

Added along with the recent Bonkies, starring cute little monkeys, and King of Dragon Pass, in which the Duck people are very important, as well as the presence of many other beast folk of different kinds.

If it counts, Lands of Lore has Dracoids, lizard-like humanoids, and Hulines, cat people.
https://lands-of-lore.fandom.com/wiki/Ascendant_Races

It doesn't take place on Earth, but by the setting's lore, most of the major factions and many of the minor factions and some wildlife are either explicitly human (originating from Earth) or engineered from those same humans at various points (possibly while still on Earth), so factions like the Therians aren't actually aliens as such.

How about Divinity: Dragon Commander (link is to the imperial edition)? The game features lizard people as a race, and a lizard councillor, lizard general, and lizard princess as characters.

One thing that I didn't ask before but maybe I was wrong. Dragons doesn't counts, right? in that case we can add more games starting i.e with Panzer Dragoon but I think that mythological, fantasy and prehistorik creatures like dragons and dinosaurs doesn't count as the kind of animals we are looking for on this thread.

Prehistorik 1 + 2
https://www.gog.com/game/prehistorik_12

I think dragons don't count unless there is a game about a Komodo dragon :)
We could make a dragon list too. I of the Dragon, Dragon's Lair, Cuphead, many fantasy strategic games that have dragon or dragon like units. Maybe a double list for proper dragons and other reptilian creatures might be useful for some gray area creatures and avoid the eternal "this is a wyvern not a dragon" debate.
Oh, so Time Commando as well, at least the prehistoric level has a jaguar and I don't remember what else. I never reached over that section of the game.
But now we need a furry list too :)

Thank you all, let's see the additions to the list:

Lands of Lore 1
Lands of Lore 2
Lands of Lore 3
Age of Wonders: Planetfall
Divinity: Dragon Commander (I remember there are lizard races also in the other chapters of the saga, can anyone confirm?)
Prehistorik 1
Prehistorik 2

@nicohvc: Dragons are excluded because they are mythological creatures, but dinosaurs are not, because they are prehistoric animals. Now that I think about it, Turok should be then included.

Turok
Turok 2: Seeds of Evil

@Dogmaus: A single jaguar is little to include Time Commando in the list, the game seems more about time travel than anything else, but let me know if you find more evidence of the inclusion of other animals.

Triple Town also seems like a good addition to the list.

Yep, in Time COmmando there are golrillas, tigers, bears, those are enemies appearing in a the first 15 minutes of the game, lacking any depth and importance. Not a worthy inclusion after all.

a giant bear was the 1st boss, then in Rome a bull... then the next boss that I remember beign an animal was the.. last one or near the last one and well ... spoiler alert... some kind of dolphin?

I can't remember too much because I beat the game around 96/97 and I was a kid.

well in that case Turok games as you said. I've omitted because wasn't sure if we're including dinosaurs.

I'm going again with Ys 8, is full of dinosaurs (not in early game) and also you have gorilla and a pelican as NPC. You can give fish to the pelican and it gives you items in exchange while the gorilla helps you to learn new moves. After midgame the game is plenty of dinosaurs called "saurians" in game. You can distinguish ankylosaurus branchosaurus, T-rex, parasaurolophus, velociraptor and much more (I'm sure that I remember a pterodactyl and a triceratops but not sure about in what situation, other dinosaurus I've remember the exact spot)
Saurians are a very relevant piece of the whole game story. I don't want to spoil too much.

Several of the Tomb Raider games would count: at least in Tomb Raider 1, a majority of enemies were different animals. According to WikiRaider's list of enemies, all of the games except Lara Croft and the Guardian of Light feature some animal adversaries, although I would say they are more prominent in the original games 1-3.

Because he is a robot created by the professor, not a real dog.

Of course this belongs here
https://www.gog.com/game/inspector_waffles
when it's released that is