While its not exploitation for commodity production, we could call it exploitation for entertainment value / comfort.

The power imbalance def exists, but its similar to that of parents and children, and its difficult to generalize that into “necessary and always harmful.” And of course there are plenty of house pets that have a lot of freedom and comfort, and the “entertainment / comfort” exploitation goes both ways. The main thing to me is they’re neither servants producing use values or commodities, or commodities themselves (unless its through a breeder).