On stage all you have are the words to tell the story.
I disagree with that. You also have the physical presence of the actors on the stage, plus the physical presence of whatever design elements the production uses. The playwright doesn't always have control over these elements, but whatever the playwright writes that is integral to the story being told should turn up in some form or other in any decent production.
Look at Samuel Beckett's Act Without Words I and II for extreme examples of a playwright using the resources of actor and staging to tell a story that doesn't involve words in the performance, although of course Beckett had to use words (as well as pictures) in the script to convey to the production team what to perform.
Most plays do involve actors speaking words, but those might not necessarily be the most important aspects of the performance.
Plays are usually linear without a lot of flashbacks and jumps in time which confuse the audience.
Or, the playwright (and the director and designers) need to be very careful about what techniques they use to indicate to the audience when time has jumped forward or backward. But the same is true of film or of words on the pages of a novel. The specific techniques and conventions may differ.
E.g., the lighting designer can be your friend here.