Architectureimage-identification
It's like a building on top of a roof. I don’t know how to describe it too well, but you can walk out of it and be on the actual building's roof. This building thing is always on a roof, and can have AC coolers on top. Sadly I’m ill so the name is lost to me. Help?
There is a specific name for it: pandiculation.
A stretching and stiffening of the trunk and extremities, as when fatigued and drowsy or on waking, often accompanied by yawning.
Joseph Ducreux pandiculating; self-portrait ca 1783
Note: While stretching is more common, it is also more general. OP didn't specifically asked for a common word and there are details in the question. Pandiculation is a tailor-made word for this specific movement. At least, you learned a new word if you didn't know it.
If you google images of covered courtyard, you get many images like this:
Many of these images show an area between two large buildings, with a latticed glass roof. Maybe this is enough to convince you that covered courtyard works as a description.
More specifically, such a glass-covered courtyard is called an atrium, which is probably why this word sprang to your mind. Many of the spaces depicted in the linked images might be called atriums.
Further, if you google "atrium between buildings" you get many results which depict spaces like the ones you describe. This should convince you that atrium is, if not the perfect word, a very good one.
The following photo, for instance, shows an atrium between the IBM Building and Trump Tower:
Best Answer
Although the most common use of the word penthouse is the biggest, most luxurious apartment at the top of a tall building, in British English at least, it is also used to describe the building your photo. From Collins Cobuild: