That means you can play with no wires when the Chromecast Ultra is hooked to your TV, but if you want to play on other devices, you will need to connect a cable to the Stadia controller to use it. The Stadia controller is the only first-party hardware that the service offers at this time, and it features Stadia-specific shortcut keys and integrated WiFi.
Google has stated that when the controller is plugged in via a USB cable, it works as a standard USB HID controller. Google notes that the controller "may work" on other platforms as a USB HID device depending on the game and setup. The assumption before this was that the Stadia Controller would work wirelessly on other Stadia platforms like Chrome laptops and Android smartphones or tablets.
The Stadia Premiere Edition bundle ships with a USB-A to USB-C cable for connecting the controller to laptops, but that cable will require an adapter to work with Pixel 3 and Pixel 4 smartphones. The "at launch" caveat would presumably indicate that functionality sans wires with other devices may land later.
Google is talking up controller functionality via USB-C and Bluetooth audio being added post-launch. Google recently announced Stadia would launch November 19th and that the service uses predictive AI to anticipate user input and reduce lag.