What do you mean "legally required"? E.g. is there a law that says that specifically, or a common interpretation of a law that says something vaguer, or a common clause in employment contracts, or were you being metaphorical and it isn't actually legal?
I'm from the US, and this sounds very strange to my ears.
The OP just decided to strangely translate a clause that asks for employees to not demand work during cation (the usual US "I'm still reading my emails") and that they cannot work at another job in that time.
I don't have the immediate texts at hand but I cite sources in my guide about taking time off in Germany. The law is very unambiguous about what vacations are for. A nice example is that if you get sick during your vacation, it counts as sick days and you can use your vacation days at a later time.
Literally, it's about preventing taking a second, paid job during vacation from your first employer. So it's not entirely clear whether this is about protecting employers or employees. As far as I know, non-competes for blue collar workers are uncommon (or at least they used to be).
I'm from the US, and this sounds very strange to my ears.