You'll find a pointer to a discussion of the VDH license here:
https://groups.google.com/g/video-downloadhelper-q-and-a/c/BzPLK2YyL-s
But no, you don't need another license. Given what the license does, it's unlikely the
license affects pretty much any problem, as you will agree if you read what I pointed you
to.
It's pretty hard to say what might be going on here. I'd say you probably have to sit
the 2 computers side by side & go through every single VDH parameter one by one to see if
anything might be different between the 2 systems. Even then, it might not solve the
problem. I don't have W10 so I can't be a whole lot more help here.