The error shows that for some reason Spine is unable to download the update file because it can't write the update file. Please try rebooting, in case some other software is preventing the update file from being written.
Also your Spine launcher is version 4.0.34. Please try downloading the latest Spine installer from your Spine license page and reinstalling. This will give you the latest version which is 4.1.12 and that may work better.