[elliptic curves, curve25519] Can someone please explain the significance of theorem 2.1?

[Reposted from r/math]

I'm reading this paper:

http://cr.yp.to/ecdh/curve25519-20060209.pdf

and trying to understand the significance of theorem 2.1. I understand elliptic curves in general, and curve25519 in particular. What I don't understand is what theorem 2.1 has to do with anything. As far as I can tell the theorem says that if you take a point on the curve Q and perform a scalar-point multiplication by any integer n, then the result has a unique x-coordinate s. But 1) that seems tautological by the definition of scalar multiplication and 2) I don't see how that result matters in any way to anything that anyone would care about (like security). Does anyone here understand this theorem well enough to explain its significance to me? Thanks.