yeah, haki means willpower. they share oden's will and are his subordinates, as samurai their entire existence is devoted to their lord, oden. the only reason they're alive is to carry out oden's will, and they all plan to die carrying it out. they're the only ones with "oden's haki". zoro is just a samurai from somewhere else, who is respected by the kozukis enough to carry the blade of a dead master and skilled enough to use it
To these guys though it seems like Odens spirit is literally feeding them his dead haki.