Normally VMware offers only the WebClient as standalone on Windows but there is a nice way to run the Webclient on linux and save the license costs for the Windows machine.
Install your Windows vCenter including SSO. As next step you import the vCenter Appliance and configure the SSO to use the existing SSO of your vCenter. Afterwards you only start the Webclient in the vCenter Appliance and keep the vCenter stopped. Now you have a full supported Webclient running on Linux.