I think this sentence is incredibly misleading. As a non-Hungarian speaker it could very easily have been taken as a way of saying "It is not evening here", a sentence that would actually make sense. As it is, this sentence would not ever occur in either the English or Hungarian language.
I think the Hungarian sentence "Itt nincs este" can mean both:
There is no evening here. Yes, this a fictional world without night, or you are in the North Pole in the middle of summer:)
It is not evening here (right now) Like, you are talking with a friend in Japan: Oh there is already evening there? Here, it is not. Maybe, "Itt még nincs este" = "It's not evening here yet" would be better here.
I think the more correct English sentence would be "It is not (the) evening here".
Otherwise, yes, it stands for "there is no", "have no", "don't have" and the like. Also, speaking of time and weather, it could stand for "it is not".
It is not cold (outside) - Nincs hideg. - There is no cold.
It is not late - Nincs késő
It is not 9 o'clock yet - Nincs még 9 óra.