The word 'theater' can have multiple meanings, but in a medical context, it often refers to an operating theater (also called an operating room in the United States). An operating theater is a specially equipped room in a hospital where surgical operations are performed. So, while 'theater' by itself does not directly mean 'surgery', in a medical setting, 'theater' is commonly used as a shorthand for the place where surgeries happen.
In summary, 'theater' can mean surgery only when used in the context of an 'operating theater', referring specifically to the location where surgery is performed, not the surgical procedure itself.