I just registered again with a new email address, there's no free player option, they say you can get a free licence after registering but all I can find is the paid version.
There is no "free version" of VMware Fusion specifically. The only difference is the license. Fusion, Fusion Player, and Fusion Pro are all the same download. Just download the paid version, run it (with the 30 day free trial) and enter the free license information you receive after registering.
I agree that the VMware website is atrocious and does not make this clear at all.