Ok, I read it again. Slowly. Same conclusion.
Let's break it down. Slowly.
i was booted from the game
So he didn't make a move on turn 1, and was booted and became an AI.
when round 1 ended
While waiting for the player to get booted, everyone else made their moves. AI made the move for the booted player.
everyone voted to end
Upon realizing that the last player to move didn't in fact make a move and got booted, everyone VTE'd.