Tiers are based on my preference not what I think are the best games... Tier 1 stuff I like the very most anyways...
Tier 1 Morrowind/Mortal Kombat 11/Brawlhalla/Warframe/WOTLK era World Of Warcraft/Assassin's Creed Origin.
Reasons... MW the world, the story, the characters the game mechanics. The Khajiit especially with the Cathay that jaguar khajiit mod. MW is the TES game I feel the least need to mod to like... I love the game mechanics in it that probably statistically annoy you. I like overcoming the miss miss miss combat, the limited magicka, being creative about cliff racers/etc. I love the wonderfully creepy, dirtier world design.
Acrobatics and jump spells are so deeply entertaining to me. I was also super fond of Vivec City and Sadrith More particularly, and I loved the alien mixture of wastelands, with swamps in some regions of Morrowind. And Mournhold/Solsthiem were icing on the cake. And I loved how vastly inhuman the Khajiit were physically that is.
MK11 I love "feeding" people to Kotal Kahn. I'm currently not very good at MK11 but when I do play good I love watching Kotal Kahn go panther mode and maul people. Motivates me to try and practice all day if I could.
Brawlhalla
Asuri enough said... Feline character with claw weapons. I quit like this game.
Warframe
Valkyr I love the character her past her abilities, the Gersemi Skin. The Bastet helmet. The claw abilities. I like how much climbing and stealth there is and having a pet Kavat. Very interested in Khora too.
I love how it has all these factions fighting and the infested, and the mixture of shooting and melee. Loki, Volt and Oberon are fun but Valkyr is my favorite.
Love all the modes including assassination, defense, survival, stealth and just plain exterminate.
WOTLK was my favorite expansion. I loved being a NELF feral druid with a pet kitty following me. I liked casual dungeons, random bgs, world pvp, and just doing my thing in the open world. I liked to RP even though I wasn't super chatty. Loved Emerald Dream server the most, immersion of RP but deadly jungle feel of a world pvp server.
Assassins Creed-Bayak as Sehkmet... Run around as a black humanoid cat in an assassins creed basically in that costume, extremely fun thing to do. With the Fallout 4 cat costume mod I'd probably rank it here.
All the tier 1 stuff are games that really feed my feline therian instinct itch. Stuff like playing as a feline, climbing like one, and just general great gameplay to go with it.
Tier 2 Oblivion/Skyrim/Zelda Breath Of The Wild
Oblivion is both literally and in a lot of ways midway between Skyrim and Morrowind. I'll mod it up and play it again eventually. I liked the other TES games art style and world design frequently, but it did have a happy medium in game mechanics, and I loved the Dark Brotherhood.
Skyrim's game mechanics are so basic I have to restrict myself to an extremely specific playstyle to avoid getting bored easily... But there is a very specific personal playstyle I like, and I love watching my Khajiit sneak murder and escape basically. Bound Weapons I like to roleplay as being like bound claws, and I only like bound melee weapons in Skyrim anyways.
The world design music graphics and visual customization partially compensate for the gameplay issues.
Regardless of the game I always like to customize my character to resemble a black jaguar as closely as I can. If that's not doable for whatever reason though, I'll more than gladly substitute a similar equivalent feline species. IE Leopard, Tiger, or even Cougar or even space alien feline. A large equivalent feline is satisfactory to me to play as.
Breath Of The Wild has no playable cats in any way, but it has tons of climbing, amazing gameplay and an amazing world and story hence it gets listed here.
Tier 3 Fallout/Deus Ex/Super Mario RPG/Ocarina Of Time/Majoras Mask/Perfect Dark 64/Planetside 2/Team Fortress 2/Mario Kart on Switch/Thief Series/Dishonored/Halo 2.
These games I just plain like. Even if I can't have the character design I'd ideally want, I like the games themselves that much.
Super Mario RPG is just a nice game I have great nostalgia over. I loved Perfect Dark multiplayer and I loved it's storyline, yeah a shooters storyline.
And I was quite fond of Halo 2, my favorite part was being the Arbiter with his cloaking device and clawlike energy sword. Planetside 2 because causing chaos as an infiltrator is extremely fun and amusing.
Fallout 3 and later Fallout games for the gameplay world and claw weapons. I like the story design and gameplay Dishonored and I liked Thief Deadly Shadows a lot. Gameplay music design and story.
Deus Ex I always liked for many reasons, I started playing it cause I thought the stealth first person and cybernetics were cool and always loved the story of it. Started with Invisible War, and quite liked Human Revolution.
Team Fortress 2 maybe cause I like first person shooters, I like the ways it is "silly" I started when it was free and was blown away a free to play game was so good. I specifically liked Spy and Demoman and liked the fact it has a Furry Server. I also really liked briefly playing the more modern Pokemon games, and collecting cat Pokemon in them too.
Favorite Android Games are another thing altogether.
Those are Might And Magic Elemental Guardians, Cyberhunter, Ravensword 2, B2B Extinction, Zombie Safari, Champs, Morphite and Cats Of The Forest.
Cyber hunter just for solo competitive and similar thrill to being a Planetside 2 infiltrator but with climbing. Ravensword 2 cause it's kinda like a TES game before Acrobatics were removed, it also has stealth and an eating survival system. Morphite cause it's like a mobile free to play No Man's Sky kinda with an adorable kitty robot companion.
Might And Magic cause I like collecting digital felines, Cats Of The Forest self explanatory cat survival game that's pretty good for a modern Android game. Zombie Safari cause I think it's pretty good for a free Android game, hunting zombies and you can leave the vehicle which I like a lot. Champs all cause I like watching Jag succeed in combat.
In short I usually like videogames primarily for theriantropic reasons but it also goes a little bit deeper than that.
I like Legend Of Zelda games a lot specifically the ones I mentioned. Story music gameplay music memories all that stuff.
On the subject of WoW I like a lot about the game. I like the Feral Druid class specifically the huge world the fact even animal forms have emotes and that you can play in them all you want.
I'm somewhat conflicted about how class balance and design is handled though. And all that said atm I only have an Android S6 so I only currently play Android Games.
I think I'd probably like TES Blades but my phone is too old to run it. I think I'd like Elder Scrolls Online but last time I had a computer that could run it, it was in Beta basically if I remember right.