These rotary encoders use a quadrature encoding. In their rest state both signal pins are disconnected. As you turn the shaft, the common (ground) pin is first connected to one signal pin, then both pins then the first signal pin is disconnected and finally both are disconnected as you return back to a detent. The Zynthian decodes this to detect direction and rotation, one detent at a time. The “Clk” and “DT” pins are actually just these two signal pins. As long as you connect ground to the common pin and each signal pin to a GPIO then assign the pins in the webconf it should work. It is possible that it will work in reverse if the pins are reversed but that is simply resolved by reversing the configuration in the webconf. The switch is activated when the shaft is pressed connecting. This needs ground on one side and a GPIO on the other.
Checkout the link that @wyleu posted. He has made this work.