That that mean, that it works elsewhere (where?), but not in WinSCP editor?
Correct. I used the AutoHotkey script provided there, which(If I understand it correctly) replaces the shift+scroll behavior with the behavior that would be associated with having a horizontal scroll wheel.
Without the script, WinSCP Editor scrolls normally when holding shift and using the scroll wheel. With the script enabled, WinSCP Editor does nothing when using shift+scroll wheel. I take the fact that the behavior changed as a sign of the script doing its job.
With the script enabled, I have tested Shift+Scrolling on Opera Web Browser, Google Chrome, Winamp, IntelliJ Idea, and Audacity, and it has worked.
On the other hand, I have also found multiple programs it doesn't work with, that also use normal scroll as the behavior when the script is disabled, but do nothing with it enabled. It should also be noted that multiple(possibly all) of the programs I successfully tested with the script also allow shift+scroll to act as horizontal scroll without the script.