You would think that a streaming video app for a TV channel would support Google's TV platform, but before today you'd be mistaken in the case of Showtime Anytime. There is finally a version of the app with Android TV support.
This app differs from the confusingly named "Showtime" app—you need a cable subscription with Showtime to use Anytime. The other Showtime app is for the channel's standalone monthly streaming plan. The new Android TV app is under the main Showtime listing, but it will download an Android TV-specific APK on your compatible device.
We've got the Android TV version of Showtime Anytime up on APK Mirror if you want to sideload it. Otherwise, you ought to be able to find it by searching on your Android TV.