just a quick clarification, since it specifically says it does not stand if "you lost dominance" does he stand if no one wins dominance? i'm a bit unsure if there might be a difference between you lost and no one won even if its just from a rules lawyer-y stand point.
Knight of the Red Fork
He gets to stand if no one wins dominance. Compare this to the refugees that say "If you do not win dominance...."
My inclination is that Staton is right (the refugee comparison seems like a good one). I can't find anywhere in the rules where winning and losing is spelled out explicitly, but I think the rules are relying on the common English usage of win/lose. So for anything (ie Initiative, Dominance, Challenges) where one player wins, all other players lose. If for some reason no player wins (as happens in the case of a tie for dominance), then no player loses.