While this kind of sucks, I can't really say it isn't within their right to do so. A story based game isn't too different from a movie -- gameplay is one thing, but cutscenes aren't exactly transformative work. If they don't want those shared, it's within their right...well, not to.
I don't think this is a smart decision, mind. People are used to be able to stream games and frankly with a game of Persona 5's length, I don't think people are going to just watch an entire Let's Play of it. That said, I do understand the argument for people not wanting to buy story based games after watching LPs of it. I mean, I didn't get Last of Us for a while because after watching a let's play of it I felt no urge to, even though beforehand I was very interested in it. I only ended up playing the game when the ps4 version came bundled with the console. Granted, given how well the game sold there's also the natural counterargument that the people who lose interest in the game are made up by the people made aware of the game in the first place due to how popular youtube videos are. I think that's a fair argument to make too.
I just don't think the matter is as simple as "I bought the game, I can do what I want." I think they are approaching this the wrong way and this isn't a smart decision, but I don't think it's right to just dismiss concerns that LPs of story based games can keep people from buying them. Friends of mine...and I myself if I'm being honest have totally fallen into the trap of "Hey, gonna go watch this LP for a bit before I get this game...wait, watched all of it. All that interested me about the game was the story, so eh, I'll get it on sale maybe?"
But yeah. I understand why people are upset and I even think Atlus isn't handling this very well...but I also disagree with people saying that they have no right over the game or that there is no way Let's Plays could prevent sales. I think there's definitely a valid argument to be made there. Like, they are not being super smart about it, and I feel like this is going to lose them more money than anything else, but it just kind of rubs me the wrong way how people are acting like it's their right to broadcast the game's cutscenes.