This kind of construction is rare in English, but it does occur. It is intended to be stronger than a simple command. If I were to try to explain why, I'd note that
Nobody touch him!
is a command. It is in the imperative, as you noticed. The implication is that you do not want anyone to touch him, and you will act against anyone who tries. This does indeed capture the intent.
We strengthen it with this phrasing
Nobody touches him.
This is now no longer phrased in the imperative. It is now phrased as a statement of fact. A peculiar construction for sure. Obviously it is possible for someone to touch him (all they have to do is reach out and poke him), so how can one make such a statement?
The best way I can describe this is that the speaker is declaring what their "world view" looks like. They are announcing that they are in a world in which nobody touches him. They're not even considering what they might do if someone tries to touch him, because in their world, nobody touches him.
Both phrases act as commands, but they are slightly different. "Nobody touch him," in the imperative, has a sense of "If you try to touch him, I will try to stop you." There's a sense that there are still some rules in place. If you're not the kind of person who would kill, people generally assume you wont kill them if they try to touch him.
"Nobody touches him" is different. By announcing the world view you are using, you are implying "If you try to touch him, I don't know what I will do." You haven't thought it through. People cannot rely on you to be yourself if they touch him. You just might snap and actually kill someone over this. You don't know, and they don't know.
The difference is subtle, and my fellow native English speakers may even disagree slightly on the shades of meaning. However, I find this explanation valuable to myself because it ties closely to the grammar of the phrase itself and works well with similar phrasings. And in the end, the answer to your question is "The movie is right, but you are right also!" The form you recommend, "Nobody move!" is the most typical way of phrasing that command. The form "Nobody touches him!" is a much less common phrasing, but it is still valid.