Content purchases or streaming should not depend on authorizations.
Authorizations allow for downloads of purchased titles. Local storage of DRM content.
Please contact Apple Support on how to handle the mismatch in number of authorized computers.
There should be a [Deauthorize All] button in the account settings, to the right — but I’m not seeing that in your screenshot. That could act as a reset to authorize only intended computers after that.

Could it be that you signed in to the TV app on this Mac with an Apple ID account that differs from the one as used to register that Mac? E.g. a secondary account? (Not sure how that ‘conflict’ would be handled.)
Authorize or deauthorize your computer for Apple ID purchases - Apple Support
Contact Apple for support and service - Apple Support