They wrote a mixed technical summary and allegory, something of a prose poem. The allegorical part is concentrated in three paragraphs. These are the second paragraph, the last paragraph, and one in the middle in which people in the "Analytic Room" regard their methods as recent in that Euler is only about three hundred years old. The youngster is evidently anyone from the "Automorphic Room." So the suggestion is that progress is likely to come from automorphic methods, and no specific mathematician is indicated. My best guess on the "ghost" is the possibility of an "exceptional" character whose $L$-function could possess a bad zero. This is from the next to last paragraph, after mention of the "Algebraic Room."
Overnight my impression of the piece clarified a bit, from a pretty vague sense that the inhabitants in the Rooms were not specific people, even from the distant past. I am close to Unreasonable Sin's comment of just an hour ago. I think the inhabitants of the Rooms are ideas more than specific theorems, techniques, particular papers. So the Youngster is an idea. Note Victor Protsak's comment of ten hours ago, I think he got it exactly right. Victor is a smart man. Heed him.
For examples of this style, see the fantasy short story collections of Lord Dunsany,
especially, from 1905, The Gods of Pegana
evidently available online in full, see for instance