I believe the idea with humanoid robots is that if you have to deploy a robot into an unforeseen and dangerous situation, having a robot with a humanoid form means it's more likely to be able to do all of the things that a human could do, and get into all of the same places.
E.g. if you have a nuclear reactor emergency - especially in an older facility - most of the controls are going to be designed for a human to operate, like the valve wheels depicted in some of the challenges in this contest, and at least some of the building is only going to be accessible through doorways, stairways, ladders, and crawlspaces designed for humans.
It's the same with operating an arbitrary vehicle (another one of the challenges). Just about any vehicle that's going to be available in an ad-hoc situation is going to be built for use by someone with at least two arms and two legs, with hands that have opposing thumbs, and which is somewhere within 20-30% of 2 meters tall (or their eyes won't be able to see anything).
Sure, you could try to build all of your critical infrastructure in ways that would allow non-humanoid robots to operate it easily as well, but that doesn't take care of all of the legacy stuff that's out there, and will be out there indefinitely.
You could also build a variety of robots that are specialized to do one or more of those things without being humanoid, but that robot probably won't do very well in the other types of situations this contest is intended to simulate.
Once they work a *lot* better, and are intuitively controllable via telepresence, I can really see some commercial applications of this too. One or two telepresence androids available for remote use sitting in a datacenter would be better in some ways than having iLO cards in every physical server. Just about anything that involves a remote, un-staffed facility becomes a lot easier if your workers can "teleport" there by android instantly when something goes wrong.