Oh I'm sure I had a hand in that sticker too
and the many many others who have recommended it over the years.
Yep it gets easier with practice and becomes your normal way of speaking.
It was written in the 80s which is why all the smacking, and I think smacking is still pretty common in America too, but for that substitute the screaming losing your rag/imposing some ridiculous punishment like "no sweets ever again". Basically anything that afterwards you think "Shit, I wish I hadn't done/said that."
The punishment argument is one which will run and run. People who don't like the idea of gentle discipline like to run with the argument that gentle discipline isn't anything special or new (it's not, anyway, so I don't understand why they think this is some kind of argument!) which is why they say "Well isn't that just a punishment?" - it's easier if you can to try and not get caught into the idealogical stuff and semantics. If it's working, great. If it's not, look for something else.
That said - I would say no, that wasn't a punishment, it was a safety measure. The primary motivation for taking the ladder away was to prevent her hurting herself, not to spoil her fun.
I reckon you could have skipped the first two instructions, because they're pretty vague and don't say anything about why jumping might be a bad idea, and gone to the third about how it's OK to climb but you don't want her to jump because she could fall and hurt herself. But tricky to do that in age appropriate language. Ultimately if she doesn't understand the danger you need to take the danger away, supervise her closely around it, and/or keep her away from it, whichever combination works.
But you did handle it perfectly. And you would have been justified in taking the stepladder away after instruction 1 or 2 as well, or even after no talking at all (though the talking helps her to build up that understanding which will keep her safer in the future, so it is valuable).
My DS is 6 now and I read all of this literature when he was younger, and the one thing I wish I'd done at the time is not worried so much about following it absolutely to the letter. Good enough is good enough, don't beat yourself up. Your #1 priority is to prevent her from hurting herself or others, if you can get her to learn a bit along the way then you've done brilliantly. :)