No other language than English has expressions with equivalents for the word show to mean being in charge (“running the show”). In fact, the modern European languages (cf. R shou) have borrowed E show for varieties of theatrical presentation because they lack equivalents that would straddle the whole semantic range of this useful little word. But what the expression betrays is something much deeper, going to the most fundamental characterization of the English nation, to wit, that the whole world is a stage. Shakespeare was only putting into words what has been known about his nation from the beginning of time. (That outlook accounts also for the fact that English philosophers have no metaphysics.)
Apropos, note the spread of words like actor and player in contemporary Anglophone discourse as substitutes for participant and other words meaning ‘person in charge, important personage’. What’s uppermost for the English forma mentis as expressed in language use is “putting on a good show” and “making a good show of it,” hence the typical British expression “good show!” to signify approval.