receivers make noise
Generally radio receivers make RF noise as a byproduct of their operation. While this is also true of just about any digital device, the details differ appreciably.
I'll not give advice on what this particular watch may transmit, but to say it does not transmit because it is a receiver is inaccurate.
I'm not a pilot, but am a retired electrical engineer.
Famously Peter Wright's Book Spycatcher recounts that UK intelligence flew aircraft over England in the 1950s specifically to detect the radio emissions from superheterodyne receivers then in use by Soviet spies. That particular byproduct noise was usefully detectable at considerable range.