You know what... this is really interesting to learn about this now, because I played the hell out of Earthbound when I was younger using an emulator, but to this day I don't recall ever beating it. And it is extremely rare that I would just stop playing a game. The only game I started and haven't completed is Oblivion.
I can't for the life of me remember completing Earthbound or when/why I stopped playing it. I just watched that Youtube clip of the end battle with Giygas and I vaguely remember it, but I have no recollection of some kind of ending. If anything I remember being kind of confused. I bet I ran into that last layer of protection where it randomly freezes and deletes the saved game, and that's why I don't recall an actual ending.
Learning about this now, I guess I feel a little better about not remembering ever beating Earthbound.