Quote Originally Posted by chaika
After some verbs like "require" we use the subjunctive.
Chaika is right about this. The best version to my ear (if you actually want to use the word "require" and the conjunction "that") is

The Russian language requires that each noun have a gender.

That's what an educated native speaker might write. But the subjunctive is dying out, and I expect most people would avoid it by rephrasing it somehow:

In Russian each noun is required to have a gender
In Russian each noun has to to have a gender
In Russian each noun has a gender

The "has to have" form is the one that sounds most ordinary.