I'm not sure why some are irritated if others consider Smash a fighting game or not. The nice thing about Smash is people can play it in a variety of ways. Items can be toggled on and off, time limits/stock adjusted, individual stages selected.
My preference varies depending on the people with whom I'm playing. Sometimes, items and dynamic stages are most fun when playing with a group of people. Other times, you want to really test your mettle against a player of similar skill, and the two of you may prefer to reduce the chances of "luck" taking away control by turning off items.
Both approaches are equally valid.
As for whether we call Smash a fighting game -- sure, why not. It may be sumo-like in style, and Sakurai himself may not call it a fighting game, but you're still dealing damage in the context of combat, with the goal of propelling people toward a "fail" state, so I'd consider it a fighting game even if it's less direct. It certainly has the competitive spirit of a fighter, with a focus on footwork and fake-outs and zoning and reflexes... A high ceiling for skill, and lots of room for individual style.