This is what we found on Wikipedia regarding the Olly, Polly & the Magic Lamp:

A mime artist, or simply mime (from Greek μῖμος, mimos, "imitator, actor"), is a person who uses mime (also called pantomime outside of Britain), the acting out of a story through body motions without the use of speech, as a theatrical medium or as a performance art. In earlier times, in English, such a performer would typically be referred to as a mummer. Miming is distinguished from silent comedy, in which the artist is a character in a film or skit without sound.

Jacques Copeau, strongly influenced by Commedia dell'arte and Japanese Noh theatre, used masks in the training of his actors. His pupil Étienne Decroux was highly influenced by this, started exploring and developing the possibilities of mime, and developed corporeal mime into a highly sculptural form, taking it outside the realms of naturalism. Jacques Lecoq contributed significantly to the development of mime and physical theatre with his training methods. As a result of this, the practice of mime has been included in the Inventory of the Intangible Cultural Heritage in France since 2017.