Aren't the meat products used for pets by-products of the meat (for humans) industry? That is, isn't it the case that no additional livestock animals are slaughtered to feed pets, beyond those that are already being slaughtered to feed humans?
That is incorrect. Around 40% of fields are used to grow food for livestock, as well as a quarter of fish caught being fed to animals. I found this article saying we could slightly increase byproduct use for feed, but they are minor improvements. https://www.nature.com/articles/s43016-022-00589-6
We then analysed the potential of replacing food-competing feedstuff—here cereals, whole fish, vegetable oils and pulses that account for 15% of total feed use—with food system by-products and residues.
a distinct minority of animal feed competes with human food
Yes, humans cannot eat grass (for example), but grass is also not a byproduct. And fields used to grow grass could be used either for other (human-edible) crops, habitation or for wildlife restoration.