Learn Spanish (Latin America): Nadie escucha el grito en la noche.

Because Nadie (Nobody) comes before the verb, you don't need a double negative. If it came after the verb, you would need the double negative to make it correct: No escucha nadie el grito en la noche.

Does nadie always take a singular verb form like escucha?

Yes. Even if you are talking about a large group of people who aren't doing something, nadie is always treated as a singular subject (like he/she/it). That is why we use escucha instead of the plural escuchan.

The translation says hears, but doesn't escuchar mean to listen?

Yes, strictly speaking oír means to hear and escuchar means to listen. However, in everyday Latin American Spanish, people very often use escuchar for both. So here, Nadie escucha can mean either Nobody listens to or Nobody hears the scream.

Why use en la noche instead of de la noche?

You use de la noche when it is tied to a specific time on the clock, like a las tres de la noche (at three in the night). When talking about something happening generally in the night or at night, you use en la noche or por la noche.