Looking at your screenshot, it appears you’re trying to update from an earlier version of The Events Calendar. Have you completed the Migration to the New Event Data System?
We may be looking at some file permission issues here. At this point, I recommend that you try manually updating the plugin (see Manual Updates). To be safe, we strongly urge testing updates in a staging environment.
I’ll be closing this thread now, but please do not hesitate to bump a new thread on our way if you have further questions/concerns. This is for us to track down topics/issues efficiently and for us to adhere to the WordPress Forum Guidelines.