Sometimes, I think it can mean play like an instrument ("toca el piano," for example). Or to tap or knock ("tocar a la puerta" means to knock on the door) but I don't think there's any other meaning here. The cat is literally touching cheese. With its little paws.
I'm pretty sure there was some sentence I just did where duolingo translated toca with "feel" as an additional translation (suggestion). I tried that now, it's wrong. Can anyone explain when/why/if tocar is translated to "feel"?