That link (with the correct key) produces a 'page not found' error when pasted into a browser. I don't know if that is the expected response.
This is happening on all but two sites that I manage that run Types. This also happened during the update from last week and I had to manually FTP the plugin update to all of them, which is completely unacceptable. Two sites where it appears to have worked are on the same server as several of the ones where it won't work.
Another manual update would be needed as I was made aware that this issue has been completely fixed in our latest version of Types.
The main is that Types is the one that contains the installer. Secondly you can try this and see if it works. Go to Plugins -> Add New and click on Commercial, then click "Check for Updates" then after that process has ran, try updating the plugins from this screen.