I like going to productions like these as they are another way for me to take in story. Reading will always be phenomenally important to any writer but that doesn't mean you can't take in stories in other media. With plays particularly, you get to "see" the impact of well written dialogue and that can help inspire you with your own writing, whether you write scripts or not. You get to hear what works. Memorable lines stay with you for a reason! The goal of course is to be able to create your own memorable lines in whatever format you choose to write.
Another favourite form of storytelling for me is audio books. Being told a story by someone else is one of the great joys of human existence for me. Again you get to hear what works. If you listen to an abridged version, and you have the unabridged book version, find out what they cut and see if you can work out why. Does this have an impact on what you put into your story or leave out of it?
I don't watch a lot of film but it's a very valid way of exploring stories. Learn to spot where the Three Act Structure is in the movie you're watching!