Listfag's approved TDM media list
All of these games include significant TDM characters or stories. They are in no particular order.
Monster Collectors
Pokemon
You surely already have strong opinions about it.
Digimon
Features many cute TDM monsters that can evolve into hot women or kaijus. Specifics depend on which game.
Yokai Watch
Short lived series about finding ghost mascots.
Palworld
Pokemon but it's a survival sandbox with guns, slavery, and modding.
Playable TDM
Vividlope
Stylish and surreal gravity bending puzzle game with cute bunnies.
Kero Blaster
The other platformer made by the creator of Cave Story.
TDM Companions
Cave Story
Classic freeware platformer adventure featuring TDM bunnies dogs Mimigas.
Animal Crossing
Mainstream gateway drug to TDM with many different animal villagers.
TDM only settings
Makemon
RPGMaker game series made by TDM artist Bayachao with many TDM characters.
Licensed games
GBA Hamtaro games
"Hamtaro Ham-Ham Heartbreak was directed by Miyamoto is an absolute gem of a game with loads and loads of personality and soul and Hamtaro is the second core pillar of chibi/TDM style after Sanrio"
I personally don't think the hamsters are cute, but maybe you do.
Jewelpets games
Rhythm games and life simiulation games for the DS featuring jewelpets, magical creatures known for their lewd inuendos
JRPGs
Disgaea
If you're not too evil, you become a cute penguin when you go to hell.
Persona 5
Morgana is TDM cat in dungeons, and a normal cat in the real world. He lives with the player character, and has unrequited love for a human woman in the main party.
Online Games
Atlyss
RPG with TDM player characters that can be customized with all the right sliders. Can be played Singleplayer or Online.
Webfishing
Play a TDM animal and fish with friends or strangers.
Porn
RAO's doujin catalog
Vore doujins that are unusually popular with TDM enthusiasts despite almost none of them being translated. They feature Pokemon, Pals, and Original characters.
Other
Super mario world romhacks
Play as Melody https://www.smwcentral.net/?p=section&a=details&id=37004 https://www.smwcentral.net/?p=section&a=details&id=38931
Or Mootcat https://longc.at/vhacks.html
Promise Mascot Agency
Open world RPG where you can recruit many strange living mascot costumes.
Tamagochi
Simplistic virtual pets. More of a merch line than a game.
Cookie Run
Gatcha game I was told to include for some reason.
Upcoming
Bombun
3d platformer made by popular TDM artist Kekitopu. May or may not launch with a lewd mod.
Ratatan
Spiritual successor to Patapon, now featuring TDM hero characters.