No it doesn't, it's quite clear that Ballmer can be choosing adversarially. The point is that even if Ballmer chooses randomly and the interviewee plays optimally given this, the game still has a negative expectation value, and that is enough to be sure the game is a loser for the interviewee.

The post never answers the question "so what is the real expectation value", which is a more difficult question. But I think if the interviewee chooses a number randomly from 40-60 as the first guess and does a binary search from there, Ballmer can't really improve on choosing his initial number randomly.