All YouTube contents are owned by Google. While theoretically you can play them on any supported device, it has to be kept in mind that Amazon Alexa devices aren't one of them. They do not directly permit YouTube videos to be played on their devices. Nor have they designed Alexa skills that enable YouTube to be played on these smart speakers.
Using Bluetooth and components such as Windows Subsystem for Android (WSA), there are workarounds that bridge this gap. However, from a legal standpoint, if you're going to use a third-party speaker like Amazon Alexa to play Youtube, go for copyright-free Creative Commons content.