A gesture in this sense is quite literal: a movement or series of movements of the body in order to express something. It could possibly be interchanged with sign or movement or motion, but gesture is the ideal word for such a movement, since it means a movement of the body that makes a sign or communication.
I agree with Matching Mole that your suggestions could be technically accurate substitutions for the word 'gesture' but in the context you give, your other suggestions would not sound natural in BE or IE.