In Multiplayer, if I attack all other players for lethal, who loses first?
All combat damage happens simultaneously. 


  510.2. Second, all combat damage that’s been assigned is dealt simultaneously. This turn-based action doesn’t use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it’s dealt.


802.6 is simply explaining a slight difference to 510.1:


  510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. This turn-based action doesn’t use the stack.


So "defending player" in this case means each of the opponents being attacked, in APNAP order.

However, the premise of your question may be flawed. There is no "second place" in magic. It doesn't matter which player loses first, or if it is simultaneous. If I kill opponent A on turn 5, and then kill opponent B on turn 6, opponent B isn't "second place" while opponent A is "third place". They are simply both players who did not win the game.