It's perfectly correct (see my other comment) and means that nobody has to choose ("Nikt nie musi wybrać", perhaps?). Not exactly Duo's sentence, which is more "It's not necessary to choose", but not far off in general meaning.
Shania Twain has a song, "No one needs to know" while Damien Rice sings "No one need know", both meaning "No one has to know".
And in that grammar the verbs "need" and "dare" are semi-modals and can be used in the same way as regular modals in negative structures - "No one need choose" and "No one needs to choose" are equally correct. In some constructions the modal form is possibly even more common, e.g. - "No one need ever know".
I think "no one need choose" can be correct, depending on the context. For example, if there is a claim that everyone has to choose something from a set of options, it would be correct to say "no one need choose" anything or "no one needs to choose." it is informal but it is not incorrect.