A small deviation in this scene from story to movie seems somewhat important. Until you really watch the kissing and clutching when they see each other.
Someone already pointed out that in the book, Jack bounds up the stairs and initiates the embrace. In the movie, Ennis comes running down the stairs, and he initiates the embrace and then initiates the out-of-control passion that has been trapped inside of him for four years.
Why is that nuance important? In the book, when they are at the motel and are laying with each other talking, Jack asks if Ennis thought they would get back into all this. He says he didn't and then laughs. "Hell yes I did. I red-lined it all the way to get here as fast as I could." He then asks Ennis again what he thought. In the book, Ennis is very forth-coming. He tells Jack about the day four years earlier that they parted. About nearly vomiting and feeling lost. He tells Jack, "It took me nearly a year to figure out that I never should have let you out of my sight."
This is such a key moment of the book. It is suddenly clear to the reader that Ennis and Jack are not just coming back together out of lust. They both have realized the summer on the mountain was life changing.
In the movie, Ennis mumbles, "I don't know," in answer to the question. There is no clear connection for the viewer that he was longing for this day and that he recognized the summer on the mountain was so important.
So, the fact Ennis initiates the contact at the bottom of the stairs became critical in my opinion.
