I remember this document -- it is the draft which circulated among cryptographers when NIST (or NSA) was preparing some new standard hash functions and was asking for comments about their proposed scheme. This document is obviously a rather hastily thrown together specification which is not, in any way, official (it has no attribution, no name, no 15-page legal blurb...).
My guess is that $S$ comes from older SHA-1 specifications which also used it to mean "circular left Shift" (this can still be seen in RFC 3174: FIPS documents are revised, but RFC are eternal). SHA-1 uses only rotations, which it calls "circular shifts", so the use of $S$ seems logical. It was then imported in the to-become SHA-2, and the letter $R$ was used for a "Right shift" since the "S" was already used for the rotation.
It does not matter much in practice; a notation is just a notation. Let us rejoice that the actual FIPS 180-4 standard uses clearer symbols.