You have to take it as a shortened form for il n’y a plus de retour en arrière possible. Same as for instance in the very common Pas de problème !. You can drop the ‘il n’y a" in this case to add a sense of abruptness to the negation:

J’arrive à la gare: trop tard, plus de trains ! Je sors de la gare, je cherche un taxi: pas de taxi !

The "ne" falls along with the verb, but there will be no ambiguity, the negative form is obvious just from "pas" ou "plus". In spoken French, the "ne" is often dropped anyway: it is very common to hear:

J’ai pas d’argent

J’ai plus d’argent

One might argue that the 2nd example is then ambiguous, as it may mean either I have more money, or I don’t have any money left. But plus is pronounced [plys] if if is the comparative for quantities, and [ply] if it is the negation for something that existed before. If you encounter this in written, it will be the context that will determine how "plus* should be understood.

As for possible, it is an adjective that qualifies the noun retour: Possible is placed here after the noun it qualifies. I guess that the puzzling thing here is that it is not placed directly after retour: en arrière is here "closely attached" to retour for its meaning, so it is ok to not separate them by an adjective. You could also say plus de retour possible en arrière – some speakers will possibly say it just sounds "better". If you leave out en arrière, and that you add a full verbal form again, maybe the sentnce will make more sense to you:

Il n’y a plus de retour possible.

Unlike English where traditional grammar states a verb is mandatory to form a complete sentence, a verbless sentence is possible in French where it is called phrase nominale.

The sentence means:

Don’t forget: once the engine is launched, no rollback [[is] possible].

It might have been rephrased:

N’oublie pas : une fois la machine lancée, le retour en arrière est impossible.

Retour en arrière is kind of a set expression here, like retour à zéro or even retour vers le futur. Breaking it with retour possible en arrière would make the sentence less idiomatic.

Nobody would even say Retour possible à zéro.

While rarer, verbless constructions do actually exist in English, for example:

[Once all rooms are occupied,] no vacancy!

or:

Mission: impossible