You actually don't have to be riding but you do have to be running the Zwift game app to check those steenken badges.
My "pain cave" uses Apple TV to ride on Zwift in the basement, but I also have the Zwift app loaded on my iPad - I can enter the Zwift game and go into the "garage" or check badges and what not by from the iPad while laying on the couch upstairs or killing time somewhere in the car!