Understanding and repairing kitchen shelf door based on a gas spring
Looks like this YouTube video answers the question:

https://www.youtube.com/watch?v=rp8365lEGjY

You have to release metal clips at both spring's ends to release it, and the new spring can just click in.

German name for the whole appliance is "Hochschwenkbeschlag", no idea how to call it in English.