Yes, you need a unique license for each user in Tableau Server, regardless of their role.
1 Server Administrator needs a seat the same as 1 Viewer.
When purchasing licenses under the "named seat" model, each person accessing Tableau Server (with whatever role, permissions and access) is supposed to be licensed individually.
At the volume of users you're describing, it doesn't make sense to talk about the core-based pricing model. (hundreds of thousands of dollars for hundreds and hundreds of users)
Hi Alrick -
It sounds as if you have exhausted the limit (5) of a named user license. As a result, any additional users defined to the server will be entered with a site role of "Unlicensed". If you want to add additional users, and have them defined as "Viewers", you will have to extend the range of your license.
License info here: Licensing Overview