1. Why does this mean it's fake exactly?
2. Nonsense. Nintendo gave us the DS and all handhelds that came after it. Garbage ergonomics.
3. This is the one actual point you have. It's indeed really similar.
4. What do you think Nintendo can do, ever heard of the Barbara Streisand effect? Come on now.
1. It doesn't outright mean it's fake. It's just incredibly improbable for an NX to be displaying a promo video, and a far from private one at that.
2. Whether you think the ergonomics of 'DS and all the handhelds that came after it' are garbage or not is totally irrelevant. But this leak isn't consistent with Nintendo design at all.
4. An invasion of privacy and a breach of protected images are not the same thing. It's obviously too late to suppress the pic at this point, but if this was related to Nintendo, they would have done something about it, very quickly. We all know how secretive Nintendo is about NX, and how protective they are about letting rivals get a head-start on whatever it is they've cooked up.
But by all means, believe what you want.