I've never used the auto update feature, but I tried today and got the same error. Same version- 64-bit. I did a little digging after this post and saw there was a version64.ini in the folder that had been properly updated and contained the correct https: urls:
I just copied the contents of version64.ini to version.ini and the update button now shows that I am up to date. I then got rid of the version.ini altogether, leaving only version64.ini and updating still works.
Conclusion based on what I see: the 64-bit version of the program still looks for version.ini before version64.ini, and if it finds it will use the information in that file. If version.ini is not present, then it will use version64.ini.