Because, being rich, famous, and a dominant Alpha, everyone crowds around him because they want something from him (whether they are Omegas, Betas, or Alphas). Josh, on the other hand, has always acted professionally, risking his life for him and respecting his personal boundaries, without forcing his own desires onto Chase. (e.g., 'Mr. Miller, can I help you?' 'Mr. Miller, may I continue?').
So yes, for the first time, he's in a situation where he feels he has the same 'power' as the person he's interacting with, and I believe that has moved him in some way. Chase senses that Josh views him as an equal, and not as someone on whom to force his will. According to Chase, Josh could have demanded anything from him after saving his life, because up until that point, every person he had met had always wanted something from him. But Josh treated him like a human being, not an object or a property, by respecting his 'NO'.