Well, there is a bit more of a defined difference here. When it comes to copyright claims (at least in the US, I'm not familiar with intellectual property protection internationally but I assume there's similarities), there's a few questions asked which help determine whether or not the contested material is infringing. Two major questions are 1) does the new material significantly differ from the original (such as in terms of how it is used) and 2) does the use of the new material possibly detract from usage of the old (aka if someone is making a profit off of something they used, is the original content creator not making money).

In the case of streamers using music, it can be argued that the use is different -- rather than go to the stream in order to listen to music, it is simply a small part of a different experience, leading into the second answer being that no, people do not go to streams instead of buying or subscribing to a music service. This is similar to how a restaurant or other business can play radio music; rather than make permanent copies of the music available for viewers, it is simply a temporary part of the experience (this is why copyright material is muted on twitch, as then the possibility of people going back to a stream to use music is possible).

In the case of NUA, he is both not changing the source material in a significant manner, and he is taking views (which equate to monetization) from the original streamer, as it can be argued that people will go to NUA to watch videos who might have watched the player's stream or youtube channel otherwise.

tl;dr: Your comparison is not that great, as there are significant differences in how each action is interpreted