I have the same issue, except for the version number Andreas mentioned. My message reads:
The following plugins are out of date: Events Calendar PRO 3.12.5. All add-ons contain dependencies on The Events Calendar and will not function properly unless paired with the right version.
My license key is entered. In fact, today is the first time I’ve actually seen the license key “stick”. Prior to that, I’d get this message:
There is an update available for The Events Calendar PRO but your license key has not been entered. Please go to the Events Calendar Options page to enter your license key.
I’d always get this message, even though all of the PRO functions worked. Now, like the posters above, I can’t update, even with the license key.