Unfortunately - yes, you need to have internet for a streaming TV.
YouTube TV, Sling, and others are all digital alternatives to traditional cable, but you need a high-quality internet connection to watch HD shows and TV stations.
However, you might be able to get rid of cable internet (which I assume you have) and go with 4G/LTE instead. It depends where you live, but if your LTE internet is unlimited for your phone plan, and the only time you'll be using the streaming service is when you're home, then you might be able to simply hotspot from your phone to the streaming device and get an internet connection that way. However, the speed and reliability of that connection will not be as strong as that of a regular WiFi router. Also...