It seems I have been able to resolve the issue; though I suspect only temporarily - by deleting folders in the AppData/Roaming/itch/Partitions folder. I expect the issue will reoccur in due course and I'll have to repeat this to resolve the issue, perhaps this could be looked into?
I ran into the exact same issue whilst browsing the site through Google Chrome, exact same error message, and had to delete cookie data for the site in the browser's settings in order to be able to visit the site again. Again this seems like an issue that is likely to reoccur.