JESS: What makes you think I care about you?
RORY: I don’t mean care care, like care. I mean if you like me at all . . . not like like. I just meant that if . . . if you think of me remotely as the sort of person that you could occasionally stand to talk to then you will try to get along with my mom, that’s all.
A very pertinent question from Jess. Rory acts as if they are already half-way to being in a relationship by telling Jess he has to be nicer and more polite to her mother. But as Jess notes, neither of them has said anything about having feelings for the other, even platonic feelings.
A flustered Rory quickly backpedals, but she has given Jess the opportunity to let Rory know how he feels. By agreeing to be nicer to Lorelai, he is tacitly saying he does care about Rory, at least as a friend. And by asking, Rory has let him know that she wants him to care for her.