In plays, there is often a description at the beginning of the scene that sets the scene before the characters start speaking. e.g., see the paragraph in italics here. What is the formal term for it?
The stage writing term is At Rise Description, so called because it describes the scene as it should look when the curtains lift. In screenwriting it is more commonly simply called a scene description, and follows the slugline.
In the example you gave the italicized text in the second paragraph is not part of the at rise description, but is rather an action direction.