Petz 5 gameplay video (I just snagged the top youtube search result): https://www.youtube.com/watch?v=8Hn4z1RYlrU. Just look how cute these pixels are :D
Basically you just... have some digital pets. You pet them, feed them, play with them, and breed them to create more pets that turn out as a convincing-enough mix of the two parents. That's it. There are in-game environments, but also a mode that lets your petz wander around your desktop - I never used it much, but hey.
There is also some interesting video game history around the way they designed the pets to be made of balls, and what that allowed them to do, but I'm not qualified to explain that and can't remember where I heard about it.
The only modern similar thing I'm aware of is Desktop Goose, which admittedly is also pretty dope (and a great way to prank your buddies, just sayin'). https://samperson.itch.io/desktop-goose
And I guess, almost, pokemon? Sort of? Not really. But it at least has that "collect cute animals" element to it.
Remember Neopets? I kinda wish I'd gotten more into that when it was a thing lol.
I think perhaps games like this have just fallen into the pit that "girly" games in general have fallen into, where that entire market is ignored by developers/publishers. The (by vast majority) men who are in charge think girls don't care about game quality, or that parents won't pay for it, or that girls barely play games at all (and ofc ignoring any self-fulfilling prophecy), so they just churn out cheap junk, if they do anything targeted to that segment at all. It's dumb and it doesn't have to be this way. But it's the same reason we still don't have high quality horse games, except for games like Zelda and Red Dead Redemption 2 and Shadow of the Colossus that have horses that are more developed/involved than in most games but still aren't the main focus of the game.
I'm not saying we should have more gendered marketing - no thanks - but entire categories of games have been thrown in the can because they're perceived as being girly. None of these categories have to be presented or marketed in a gendered way, nor would they be inherently bad in games - men and boys could easily enjoy them too.
Just look at how many games involve "character customization" that is just another way of saying dress-up at the end of the day (gotta have that 'don't show helmet' button, and clothes dying, and special versions of armor that just look slightly different but have the same stats!), or at wildly popular games like Animal Crossing, Stardew Valley, and Minecraft, which feature a lot of homemaking and decorating. Just look at the fact that if a dog is in a game, you'd better be able to pet the dog, because near everyone wants to pet the dog.
I'd be absolutely shocked if a really high quality horse game couldn't be equally popular, especially given how much many men and boys also like the horses when they've appeared in games where they aren't the focus (and on the rare occasion when they almost are - so many people got so attached to Agro in Shadow of the Colossus). And there are veritable hordes of horse-loving women and girls (and some men and enbies among them too) who have been yearning for good horse games for YEARS.
Heck, a horse game could be anything from a "take long rides through relaxing forests, maybe with a bit of a pokemon snap element" to "sports management game but with race horses this time" to "tricksy sports sim, or local co-op QWOP/Octodad-alike, about dressage or barrel racing or horse jumping" to "you're a messenger in a fantasy universe and you've gotta go fast but also cooperate with and not exhaust your horse, while managing your resources and time, and your horse actually has some personality and isn't just a car with legs".
This video from Moon Channel, run by a lawyer who normally talks about copyright law re. video games, does a good job of making this argument more thoroughly: https://www.youtube.com/watch?v=-BtmNI-xTbQ.
Anyway. Originally I only meant to talk about Petz, but the post kinda ran away from me. C'est la vie.