I'm no chemistry or physics expert myself, but anyway, air isn't all oxygen so it doesn't burn like pure oxygen, and I think usually some sort of other fuel is required to get the fire going strong enough to light the oxygen (at least with pure air, which explains the "whole world not combusting"). As far as I know, the oxygen is just kind of an "ingredient" in fire, not the main fuel.
Fun fact: speaking of chemistry, my dad and a few of his friends made a bunch of pure hydrogen from water in one of their garages and they got a lawnmower to run off it for an hour. By then everything had rusted too much to work, due to the hydrogen itself. Unfortunately, this was a long time ago so I don't remember it, don't know if I was too young or if it was before I was born.