If you don't have any imagination and you treat dogs as database entries then yes you might do just that. If you are only person writing it and using that code, the same.

You did not address interaction between dogs. Some other idea, how do you pass dogs to a playpen, how would they interact - maybe you want different playpens where you can send your dogs into, some playpens having food, some not having a food, different types of food. What if some other developer will have to write code to heal the dog? If function to dog.Heal() will be in some different module that you never heard of, how do you find it?

You don't want to make each playpen having "if species_of(pet)" code duplication, if pet alone can act on its own will.

Writing code in here seems not that useful here because you would really have to imagine possibilities and see how much code would go into wiring up such a world. Then seeing how having methods in object are helping organize code and in the end prevent whole classes of errors.

Building all of that as an example is just too much work for one off discussion. Just play with imagination of how much complexity you can add to a simple example and soon you will notice.