Possibly related: I'm having a similar issue when trying to run several installers or standalone EXEs.
Doing "wine foo.exe" (where foo.exe is known to be fully compatible with wine) yields:
it looks like wine32 is missing, you should install it. as root, please execute "apt-get install wine32"
A lot of Windows applications are still distributed as 32-bit binaries to avoid compatibility issues, so this kind of makes sense. But wine32 is not in the main PureOS repo because (IIRC) PureOS is all 64-bit code. So i386 isn't an enabled architecture, nor does the repo distribute 32-bit software.