What I find strange is that the examples where we fetch the .dll files seem to be in the x86 section (C:\Program Files (x86)\FMOD SoundSystem\FMOD Studio API Windows\api\core\examples\bin
and
C:\Program Files (x86)\FMOD SoundSystem\FMOD Studio API Windows\api\studio\examples\bin)
It would have been more natural to find them in a place where you expect 64 bit .dlls. For example, C:\Program Files\FMOD SoundSystem\FMOD Studio API Windows\api\core\lib\x64 or a similar path.
But if what we got is not 64 bit dlls then the error about incorrect format makes a lot of sense.
If that suspiction is correct we get to the question: Where do we find the 64 bit dlls?