Yes, it’s an eyeball, which is awesome. This pet is from the manga series GeGeGe no Kitaro and represents the Yokai Medama-Oyaji, which makes a little more sense, not that you’d need it to make sense in order to take care of an eyeball. It does a lot less than most virtual pets, and doesn’t seem to have any buttons on it. Instead, you interact with the pet by tapping on the case.
User DecepticonCrown ran one of these on the TamaTalk forums, and has posted a play log here: https://www.tamatalk.com/threads/gegege-no-kitaro-v-pet-log-comments-ok.201023/