The references listing just contains other .NET assemblies your program references and uses or COM objects, but any unmanaged code that you call though DllImport
is never listed there. As the vendor says, it's dynamically loaded on demand and don't implies a compile-time reference, that's why you don't see there.
But, that don't means that you don't need the .DLL itself at runtime. The file must be accessible at the moment your program makes the first call on the P/Invoke'd function. Look where you got the source, they must supply that third party library with it (otherwise the code is useless). A typical practice is to put DLLs together with the main .EXE so the system can easily locate them.
If you add the DLL to the project (not as a reference, but as an "existing file"), you can set its Copy to output directory
to Copy always
so that you always have it available on compilation.