Community Wishlist Cats - Please Upvote: Stray:
https://www.gog.com/wishlist/games/stray Cat Quest 3:
https://www.gog.com/wishlist/games/cat_quest_pirates_of_the_purribean This has been annonced already for Steam. I've already contacted the developers, and all I got back was that nothing is confirmed for a GOG release.
Games on GOG with Cats that are missing from the collection: A Short Hike
There's a cat NPC that asks for your help in locating his lost camping permit.
Agent A: A Puzzle in Disguise
Ruby La Rouge's black cat that shows up several times in this game and even changes sides to aid you in the end.
Alekon
This game is pretty much Pokemon Snap but since I haven't played it yet, I cannot tell you if it is on rails or not like Pokemon Snap or if you get to wander where you want. One of the creatures that you can photograph is a nekolar, which is a Cheshire Cat.
Amairo Chocolate
Cat girls (and puppy girls) with sexual content and nudity.
Beacon Pines
Beck Moedwil is the black cat that you see on the store page banner. She first shows up in Chapter 3 and is one of the game's deuteragonists, meaning she's of major importance.
Chook & Sosig: Walk the Plank
The player character, Sosig, is literally a blue cat.
Clouzy!
The game has a creature known as a cloud cat. It's literally on the game banner.
Coromon
Pokemon clone where the three ghost pokemon (Gastly, Haunter, Gengar) are replaced with three ghost cats.
Costume Quest
One of the costumes that you can unlock later in the game is black cat. In the main game area, they look like a little kid wandering around in a cat costume. In battles, they literally turn into a blak cat.
Cthulhu Saves Christmas
Each day in the city, you can work on your R’lyehtionships. One of these involves going to a pet shop, where an Ultharian (green cat from Ulthar) will ask you to rescue him.
Divine Dvinity
Besides Arhu the talking white cat, there's a quest to help a girl find her cat Cosmo. There's kitty that follows you around and meows at you in the first town. There's also lots of cats all over the world just ignoring you and doing their own cat thing. Also if you erroneously attack a cat in this game, you'll be forever hated by all cats everywhere. Some call it a bug, I call it cats know.
Donut County
There's a chef cat that runs a restaurant that is having a bug problem. You help him out by destroying the restaurant. There's a regular cat in one of the other levels.
Gibbous - A Cthulhu Adventurer
All the player characters may be human, but the most important character is the cat you see on the store banner.
Godhood
Level up your religion for the first time, select Animalism, then tell your people to go worship cats. You're welcome.
Grim Fandango Remastered
Beloved Sanspoof.
Hidden Folks
There are a total of two cats in this game.
Hidden Through Time
There are cats in this game for you to find. I know they're in the default levels, Viking Tales, Aztec Ruins and Road to Rome.
Holy Potatoes! We're in Space?!
There's a blue cat here.
Kraken Academy!!
There's an achievement in this game for petting a cat, so there must be a cat.
Lands of Lore 1+2
The cannoical Champion of Gladstone as in the player character of the first game is Kieran, who is Huline (or race of humanoid cats.)
Letters
One of things you can do in this game is just stack cats or something.
Littlewood
There's pets in this game that includes all sorts of cats.
Master of Orion 1+2
One of the playable civilizations are the Mrrshans, who are a race of humanoid cat aliens. They favor an offensive playstyle.
Monster Prom (series)
One of the characters is Valerie Oberlin, purple cat person
Neverwinter Nights Enhanced Edition
The premium module version of Tyrants of the Moonsea has a single house cat. In the default campain (The Wailing Death), you'll hear cat sounds in Port Llast but don't actually see them. House cats have shown up in a few player created modules, such as the third chapter of Prophet.
Night Call
One of your potential passengers is Crouky (a black cat), who even manages to pay for his cab ride.
No Longer Home
This game may be about humans and their relationships with other humans, but there are a couple of cats in the game that you can interact with.
Reigns: Game of Thrones
Balerion the Cat is in the game.
Snacko
Momo and Mikan (two cats) are starting a new life to revitalize a cursed island.
Sunblaze
There's a cat in this game that you can pet.
Sucker for Love: First Date
One of the eldritch horror ladies that you can summon and date is Nyanlathotep, who has green hair and one eye on a face you otherwise cannot actually see.
Tangledeep
One of the NPCs in the game is Cat'ie, who is a cat girl.
There Is No Game: Wrong Dimension
There's some cats that show up here, specifically the level where it looks like you're stuck in a credit sequence.
Thimbleweed Park
If you turn on the television in the hotel room, one of the programs is "I Love My Cat."
Wintermoor Tactics Club
The calendar in your club meeting room has a cat on it and a different cat pun each day.
Wizardry 6-8
The Felpurrs are a race of humanoid cats and available for your party.
(Special thanks goes to dtgreene for telling me about the Felpurrs.)
Yakuza 6: The Song of Life
Nyan Nyan Cafe. Rescue a bunch of cats to go live at this cafe, then you can visit periodically to feed them
Yakuza: Like a Dragon
Not as good as Yakuza 6, but you still get to rescue cats.
Honorable Mention: The Elder Scrolls V: Skyrim
There's a mod called "A Cats Life" that allows you to be the Crazy Cat Hero that you were always meant to be and live your best life by adopting and providing for cats. It even adds vendors that sell cat stuff for you to purchase for your cats.
edit -- This is by no means 100% complete. There's probably cats lurking about in games that even I am not aware of.
