Fighting games are generally games focused on 1-vs-1 combat against human or computer controlled opponents, where each player is tasked with draining the opponent's health until they are defeated.
I personally regard Smash as a fighting game but I can see why some people don't, as it heavily eschews the typical health-bar-draining format for a more unorthodox platforming style. In Smash, a character with low/non-existent damage can still be instantly killed by falling off a ledge or botching their recovery, yet a character with high damage can still survive and put up fight. At no point in a match are they are guaranteed to live or die. This makes it substantially different from a typical fighting game.