Learn Spanish (Latin America): ¿De verdad dicen eso?

Because this is an impersonal sentence. In Spanish, using the "they" form of a verb without ellos or ellas is the standard way to talk about what people in general do or say. It's just like the English general "they" in "they say it's going to rain." If you added ellos, it would change the meaning to ask if a specific, previously mentioned group of people say that.

Could this also translate to "Is that really said?" or "Do people really say that?"

Exactly. English often uses the passive voice ("Is that said?") or the word "people" to express a general action. Spanish strongly prefers this impersonal "they" form (dicen) to express the exact same idea.

Why use the neuter eso instead of ese or esa?

You use the neuter pronoun eso (meaning "that") when you are referring to a concept, a situation, or a statement, rather than a specific physical object with a masculine or feminine gender. Since "that" in this sentence refers to a phrase or idea someone just heard, eso is the correct choice.

Can I use realmente instead of de verdad here?

Yes, you absolutely can. De verdad and realmente both mean "really" and are interchangeable in a sentence like this. De verdad is just a very common, natural-sounding phrase in everyday conversational Spanish.