They need to know how many different subscribers listen and, then, for how long. Based on the total listener count, they can compare with the Stern count to see how many subscribers make Stern an important part of their subscription and then calculate the ROI based on the total cost of the channel.
While they can't get average listenership and total listeners from most satellite installs, they can get the streaming count and extrapolate / project.
That is statistically reliable enough for them to bet hundreds of millions on. They obviously felt the name was big enough to give him the Summer off. The management at Sirius / XM calls on their analysts to help them make a decision, and we know that they have always done a pretty good job at creating a product that subscribers will pay for.