I interpreted it as Harry being jolted out of his all-consuming inner monologue by Dumbledore suddenly touching his shoulder while he wasn't paying attention to Dumbledore at all.

But Harry didn't see anything helpful he could do using spells in his lexicon, Dumbledore wasn't being very cooperative, and in any case this was several minutes after the critical location within Time

"Harry," the Headmaster whispered, laying his hand on Harry's shoulder. He had vanished from where he was standing over the Weasley twins and come into existence beside Harry; George Weasley had discontinously teleported from where he was sitting to be kneeling next to his brother's side, and Fred was now lying straight with his eyes open and wincing as he breathed. "Harry, you must go from this place."

He wasn't paying attention at all to Dumbledore, Fred, or George, and he's startled by their sudden agency. To me it seems more likely that leaving off in the middle of a sentence as he's startled is a stylistic choice, rather than a particularly meaningful missing period.