I agree that the entry is wrong.
The point is the difference between 'your step' (= Tritt, Treten; an action, something you do) and 'the step' (= Stufe; an object, something you see).
To watch your step literally is to watch where you are putting your feet, how you are walking; to step carefully. It's usually said because of rough or uneven ground, a hole you could fall into, or something you could trip over. Of course, you can also say it when the obstacle, the reason for the comment, happens to be a physical step, but it doesn't mean that step, it means the steps you take with your feet.
To watch your step figuratively is to proceed with caution, tread gingerly, be prudent, behave carefully, etc.: Watch your step with the new boss, he's a maniac about details / has a very short temper / etc.
Both the literal and the figurative senses with 'your step' are AE/BE and can be translated in many ways; namely, almost any synonym for 'Pass auf' (or the equivalent with Sie).
Warnings with 'the step,' about a step in the sense of Stufe, however, may be different in AE and BE. 'Mind' in the sense of 'watch out for' or 'be careful of' is BE only; that's why so many American tourists in London are amused enough by 'Mind the gap' to buy the T-shirt, and 'Mind the step' falls in the same very BE category. For us, 'mind' means 'take care of,' 'look after,' as in 'mind the store' or 'mind the baby.'
There are several possible ways to express 'Vorsicht: Stufe' in AE: Watch the step, Watch out for the step, Be careful of the step, Look out for the step, etc. The most common on a sign might just be 'STEP' or 'Caution: Step'; the others are more what you would say to a person walking. I don't know which of those are AE only and which could also be used in BE.