Guess what? I've discovered that a year later, someone else (a cousin) emigrated apparently using the same Russian passport! And this time it was clearly the "real" Elie. The first user must have mailed the passport back home after it got him to the US.
It further occurs to me that the reason may be that both men were in their early 20s, hence eligible for military service. The Russian government was very strict about emigration for such men, perhaps especially in the immediate aftermath of the Russo-Japanese War.