When Montag looks at the empty McClellan house, what does Beatty intuitively understand?
I assume that you are talking about the episode in Part One where Montag is playing cards at the firehouse. In this passage, Montag sees that Clarisse's house is empty and then, in the next paragraph, is at the firehouse playing cards. So Montag and Beatty are not together at the McClellans' house. In this scene, what Beatty intuitively understands is that Montag is feeling some sort of guilt and unease.
When Montag sees the empty house, he becomes uneasy about himself and his role in the society that he lives in. He is starting to feel guilty about his job. A little later on in this part of the book, he will ask Beatty what it would be like if their own houses and possessions got burned. He is clearly feeling empathy for the rebels like the McClellans.
Beatty seems to intutively understand this fact. He realizes that Montag is starting to have doubts and may be on the verge of going against the norms of the society himself.