Why does VMWare Player always appear "always on top" of other windows?

That's the behavior of full-screen apps, unfortunately. It's not VMWare specific. Apps like to open on the primary monitor, which is also where full-screen apps like to be full screened. Short of running VMWare Player in windowed mode, you are probably out of luck.

You could try using VMWare full screen on your secondary display, but I doubt it is the best way to do it.

I never had any luck running a VM instance in full screen on a single display of my multi monitor setup before, I ended up using Unity function which is a much better solution. However, multi monitor within the VM itself works great, you just need to configure VMWare to use both.