There is no paid license for Types. Types is free and available on the WordPress repository. And we don’t build the demo content with it, all it does is register the Custom Post Types - it doesn’t hold any of your data, that’s in your database.
Anyway, just checked their forums and it seems it’s a bug: https://wordpress.org/support/topic/cant-update-to-latest-version
What I did to go around this bug was to download the latest version, delete the plugin in /wp-content/plugins/types and then upload the new version manually. Or you can wait until they fix it, it’s not like it was a security update.