The vast majority of (good) gentle parenting is just positive parenting, which is absolutely normal/mainstream parenting. Gentle parenting isn't something special or new. Some of the wrappers like not saying no/naughty might be but they don't really matter, it's just a stylistic
choice, much like time out/naughty step/thinking step don't change because you call it a different thing.
I would have taken the cup away as well - that's drawing a boundary. But I also think fairly basic/obvious. Perhaps the mum in the video was trying to say something against "the norm" or whatever, I don't know.
I don't get on top of the kids if they are being a bit rough and some water slops over the edge. Our bathroom is tiled so I just put a towel down and see it as saving me from mopping behind the toilet. Cups being tipped out is over my tolerance level though. I would have first reminded them to pour inside the bath, I might have suggested some game that I thought might be more compelling - see if you can pour it into this container, wash these bubbles off (or whatever) IME usually this would be enough to put a stop to it, but I would take the cup away if they were really intent on pouring it out of the bath. I would also show them the water on the floor to see that it was making a mess/hazard, unless they were in that total loo-la crazy overtired hyper mode, in which case forget it. Again I think all of this is pretty standard though? Or maybe it's not? I think Janet Lansbury would probably suggest saying something like "You're showing me you need help to be sensible with the cup" which I think is a bit passive aggressive TBH :o
DH would probably say no, that is naughty. I wouldn't say that because I have some baggage about the word naughty, but also just don't think it is very helpful as a concept. I would probably start with the positively worded sentence saying what I want (Keep the water in the bath) and then change to "I'm going to take this cup away now, I don't want water on the floor." Or maybe even just "I don't want water on the floor." It's wordy but my 3yo could follow that fine.
In fact I think maybe the difference is I would take it without giving a warning - I know that sounds a bit chaotic so I'm trying to think how to explain it. But I don't like the thing where you basically tell them "I'm going to test your impulse control now. Right, OK, you failed the test." I can already see that they have an impulse to pour water out of the bath, I know their impulse control is underdeveloped because they are little and even lower than normal because they are tired, and so I feel it is somewhat setting them up to fail to say "If you do that again I will..." I don't really want to give them a choice and then judge the choice as being right or wrong. I would rather give information and see if they are going to collaborate with me, and step in to prevent harm when necessary. If I take the cup then I'm doing it to save my floor, not because I want to deprive them of fun in order that they associate that with disobeying. I might well swap it with something else fun but less splashy. I might even distract them with something else and then quietly remove it (I would be less likely to do that these days, as I've learned more about how important it is to be clear and upfront about boundaries). I'd certainly do that for my 7mo because they wouldn't understand the explanation of the boundary anyway.
Not saying this way is better BTW, just trying to explore what my thought process is for how I'd handle this fairly common scenario and why - I wouldn't be thinking through and making these decisions on a micro level every time, it's more of a background to how I tend to act.