You neglected to mention which method you are gaming on, Steam, or Lutris. But I am going to go out on a limb, and say its Steam. Open the Steam APP. Up at the top click on STEAM, go to settings. Go to DOWNLOADS tab.
Up at the top you will see Steam Games Library, click on that. You will need to create a new Steam Game's Library folder on the HDD drive. Hit the plus sign I think it is, then navigate to your HDD, and choose that.
If there is anything on the hard drive, Steam will throw a fit and say the drive must be empty. Easiest way to fix that if it happens, is to format the drive EXT4 with the DISKS utility in the OS. Then once prepared, go and do the steps again. Add your library to the HDD drive.
Then very important, make sure to tell steam that you wish that HDD to be default. Then your done, Steam will remember to install on your HDD from now on. Hope this helps
Your Tech Support Guru