Ethically, no I don't think Nintendo has any right to that money. Games are art, which means at the end of the day, Nintendo is a corporation of artists. So I think of it like this: if an artist paints a picture, you can look at it all you want for free, but if you want to own the painting, you have to pay. So why should Nintendo get money just from me looking at their art? Seems like sort of a greedy dick move to me.
I also question sometimes whether the LP-ers themselves have any right to money. You could equate LP-ers to movie critics, who get paid all the time just for their stupid opinion, but there's still a difference. LP-ers often showcase the entirety of a game. That would be like a movie critic posting a video of himself watching a movie and commentating on the entirety of it. But then again, movies are different than games. I don't know. It's a very grey area.
At the end of the day, however, it comes down to greed (which I think we all know by now). These people are artists who got lost in the money. If you do what you love and do it with passion, the money will come. But if you make it the most important aspect, you lose sight of what's important. I think that's what's happening to Nintendo. They're forgetting how to be artists.
I hope this makes sense, I'm kinda tired right now.