Solution 3 - this is it.
Thank you, Richard!
I checked with OEM's documents, it turns out that .dll libraries are part of the software package installed in support of the device I am working with (a multi-function data acquisition interface).
And I agree with Karsten (Solution 4) - "Wellcome in DLL hell" (ho-ho-ho)
Loading on start vs. loading on demand, the trouble with C and C++ conventions
extern "C" int __declspec(dllexport) WINAPI ...
I remember going nuts learning all that, but it was a long time ago.
So the "problem" has nothing to do with Windows 10. It turned out, that out of all the computers I tested only one had the proper libraries installed for the device support, and that is why it worked.