Ah, I thought you installed the Linux version of Ansys on your Windows machine, which made no sense. Now I understand you are trying to run Workbench on the Linux computer, but have a remote Xterm display on your Windows computer using Cygwin, is that right? 

Here is a link to the pdf file for remote display support.  You will see that Cygwin is not supported.

I have successfully run Workbench on a Linux server while displaying the Xterm on my Windows computer using Open Text Exceed TurboX.  You could try the VCN Connect or Turbo VCN since they are supported.

Why do you need to run Workbench on the Linux computer?  Why not just run the solver on the Linux computer?  At my work, we have installed Remote Solve Manager on the Linux server to automate the submission of jobs to the server from any Windows computer with Ansys installed that is on the same network with the Linux computer.  The Windows computers do not need to be powerful.  If your Linux server doesn't have Remote Solve Manager installed yet, you should request it, but while you are waiting, you could manually write out the input file, copy that file to the Linux computer, use a command line to start the solver, then copy the results file back to your Windows computer. That is such a pain, you will be so glad when Remote Solve Manager is installed.