To my eye, that looks like about the ADA 1:12 pitch, so if you can do a manual ramp, I don't know why you couldn't do it in a chair, even w/o holding on (just ride on it while keeping the chair still... I also didn't see a non-powered ramp, and the sign did NOT have directions for where to find one, or an elevator...
I suspect that mostly the prohibition is legal arse-covering, where if someone gets hurt they can say

"No lawsuits because we told you not to do that..."
It shouldn't have any problem with the weight of a chair and user either, as those things are supposed to be designed to still work when fully loaded w/ passengers plus a safety margin...
I know that I have done regular escalators in my manual wheelchair (and was taught how to do them by the folks in rehab....)
ex-Gooserider