This is a good point. I hadn’t thought about it, but no - I don’t consider you a pet owner, at least in regard to the cats. Do you?
To me, a “pet” is an animal whose primary function is companionship. Fido might also be a great guard dog, and Whiskers might also be a great mouser, but the real reason you have them is because they’re your buddies. If they stopped guarding or mousing, you’d be perfectly content to just keep them around for the joy they bring you. And on preview of your latest response, I’d add - any (normal) damage they might do to your house or property is far outweighed by the pleasure of their company. You’d try to prevent it, sure, but you’d take a certain amount of scratched-up furniture and peed-on carpets as just part of the cost of having this great little buddy.
In your case, although you may vaguely like the cats, and even admire their beauty or enjoy their silly antics at times, it sounds like the only reason you have them is that they kill mice. Otherwise, you wouldn’t bother to spend the money to feed them, right? And further, you don’t actually keep them, if I understand correctly. They hang around because there’s food, but that’s more like putting out a bird feeder, to me. I wouldn’t say that the cardinals that visit your back porch are pets, and neither are the cats.
To my mind, what you’ve got there are - at best - farm animals. They do a job, and in return, you feed them and offer some shelter so they stick around. That’s a totally fine and reasonable relationship, but they’re not pets.