Not sure how I missed the fact that you're running OSX inside the VM
Are you able to successfully run AirPlay mirroring from your actual host's operating system?
Do you have a USB>Ethernet adapter? I would try connecting it to your Mac while the VM is booted up and when prompted.. select to connect the USB>Ethernet adapter directly to your VM. Then physically connect your adapter to the same network that the AppleTV resides. Are you able to use mirroring from the VM now?
If you don't have a USB>Ethernet adapter, I'd probably trying messing around w the VMware settings of your guestVM. Is it set to "Share Mac network?".. Try "bridged" mode
I'm not sure what requirements there are for AirPlay mirroring to work, but I am suspecting that it's a networking issue