While Rory is arguing with Tristan, Dean appears. He has slowly put together the pieces of the puzzle: Rory came to his house, and made a speech in public about how hard it is express your feelings. From this he correctly deduces that Rory wants to see him, and really does have feelings for him, so he drives to her school to confront her.
Why he didn’t just go to her house is not clear – maybe he was scared to see Lorelai, or word had got around that Luke was spending all his free time, and some time that wasn’t free, hanging around Lorelai’s house. It also seems to have taken him a long time to ponder the two bits of information and arrive at the correct result, as it’s more than a week since the town meeting now.
Luckily security at Chilton is really lax, and nobody tells Dean to get off school property or go find somewhere else to park rather than the main courtyard in front of the building. And luckily Rory happened to come right to where he was waiting, and he even got to rescue her from creepy Tristan.
Rory is glad to see him, and touched to discover that he has a Rory box of memories, the counterpart to her Dean box of memories. She is finally able to say, “I love you“, although she can’t help adding, “… you idiot”, and she kisses Dean.