Getting started - Why FCM Cloud Function requires Node.js?

I've already start to use Firebase Cloud Function: I never developed on server side and I never used Node.js, so probably I'll ask you simple questions.
Now I've installed Node.js on my PC, but why I need it to use this program (as well as it is written here https://firebase.google.com/docs/functions/get-started)?
I need also to download this project from GitHub?

I found this link Serverless Apps With Firebase Cloud Functions, Sending FCM Push using Cloud Functions for Firebase, but it's not explained why I need Node.js. Searching on the web I've understood that Node.js is a server-side program which waits for events (probably this explanation is incorrect); if I have the server in Firebase, and the cloud function is on Firebase too, why should I have Node.js on my PC?
What happens if I turn off my PC? Node.js will turn off too..

Can you explain me this "basic" concept? Thank you!

via A. Wolf