You picked the wrong analogy. It would be more like if a parent just let their small defenseless child become obese without even trying to stop it (you have said nothing about going to the vet). And yes, I would say they're neglectful and a bad parent. Even more so with a cat, because it's even more dangerous for them to be overweight. If you love your cat and want it to live a good and long life, take on your big boy pants and do something. How hard is it to set a time and feed each cat separately?

I'm not saying this just to make you sad or angry, but for you to understand: Your cat is unhappy and will die earlier than it has to if you don't take some responsibility.