VMWare Player has a bug during the installation process, where you get through accepting the license agreement but pressing the Finish button doesn't complete the installation - it just does nothing. Several results on Google implied that it was something to do with needing root privileges, but the exact solutions didn't work for me.
When I used
sudo vmplayer I experienced the same bug, but after becoming the root user with
sudo su and then running
vmplayer finally completed the install. I'm not really sure what's going on there. Afterwards I could run VMWare Player as my non-privileged user and it worked fine.