> what role does a robot that has been built to run real fast play in that scenario?

It will run real fast up the stairs, I guess? Is it a good enough riddle?

The thing has no real arms, hands or carry capacity, so what would be the point?

Running up the stairs is the easy part after all. The difficult part in such scenario is lack of orientation due to smoke, obstacles like locked doors or fallen debris, unstable walls and ceilings, locating people and getting them out safely. All of those things require a good amount of autonomy, on-the-spot physical problem solving and judgement.

To this effect, the recent DARPA Triage Challenge, which has its final taking place in November this year, seems like a much more thorough and practical demonstration of current capabilities. Something to look forward to if you're interested in the current state-of-the-art w.r.t. real-world applications of robotics.