The dominant cost in Shor's algorithm is the elliptic curve point addition subroutine. That subroutine can be implemented using reversible classical gates. For that kind of implementation, approximate correctness can be verified by fuzz testing classical trajectories through the subroutine.

Note you could ask the same question about Shor's original paper: how did he show the algorithm works without running it? Running X just isn't the only way to analyze X.