They offer no hint why transiting the star could help us pick up radio transmissions. If they mean the planet going behind the star (being "occulted") would cut off the radio signal while it is back there, they should say that instead.
Signals from such a transmitter placed on a planet spinning around a foreign star would drift in time when observed from Earth, "the same as when an ambulance goes past you, the sound of it shifts from very high to very low"
What's wrong with saying Doppler, frequency, or pitch maybe?