does the family member I want to share my Apple TV subscription with need to have an iCloud account?

As was stated earlier, they need an Apple ID. You may find information in these documents useful:

How to create a new Apple ID - Apple Support

and

Set up Family Sharing - Apple Support

When they create an Apple ID they automatically get access to iCloud. Some components are free, such as the basic 5 GB online storage or iCloud Mail. Others are enhanced by subscriptions. iCloud is a whole other topic (and forum): Set up iCloud on all your devices - Apple Support

They need to have an Apple ID. Wether they use iCloud with it or not, is not important. But they need an Apple ID for you to invite them into Family Family Sharing