It's a matter of degrees, as said above. If you put your collection before everything else your life, you're a compulsive hoarder. It's fine to have certain items that you would never want to part with under reasonable circumstances, but if you'd never want to give up anything for any reason and you feel like it would literally kill you to do so, then yeah, you have a problem.
I was sort of half-watching this episode but I missed the part about the arcade collector. I wondered if it would get mentioned here or somewhere else, but I missed enough of the important details to not be able to form an opinion on it.