So any game with "PvP" is now "competitive". No. Destiny is a coop, shooter rpg first. PvP should be secondary. This isn't some real competitive game like overwatch, or rainbow six or whatever other game is built primarily for competition.
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"competitve" is up to how much effort you want to put into it and how much importance a community puts on the pvp. If you use that word to mean games like LoL, DotA or Overwatch then you're really being specific with a term that has a wider use. Trials in D1 was pretty competitive but it wasn't to the point of being a competitive sport.