The shoulder is a very complicated joint. Here are some of its parts: There are four rotator cuff muscles. The joint is also crossed by the long head of the bicep. The joint capsul is comprised of the coracoacromial, coracohumeral, and glenohumeral ligaments. There are four different bursa, by my count. The glenohumeral joint is very close to the acromion of the scapula and the subacromial space. That is just the start.
So the question is, what tissue is the person in that picture stretching? I really don't know. It is impossible to say without diving deep into the anatomy, which is far beyond what anyon we can do on this website. However, my intuition, just looking at the picture, is that this person is putting a lot of stretch into part of the joint capsul, which is a bad idea.
The glenohumeral capsul is the tissue that prevents the head of your humerus from popping out of the glenoid fossa. You don't want this tissue to be loose. It is fine to stretch the muscles around the capsul, but stay away from the capsul itself. If for some reason you believe that some area of your shoulder capsul is tight, then you should go to a physical therapist to get a diagnosis. There are some standard tests that can be performed to diagnose and locate tightness in the shoulder capsul. Baseball pictures are know to have a problem with tightness in the posterior glenhohumeral capsul. (I might have this backwards. It might be the anterior capsul, so check me on that.) If you don't have a diagnosis, then stay away from the shoulder capsul.
Finally, I have a question: Are you a prepubescent female? If not, then you should not be taking advise from this young lady. I would recommend an adult such as Mike Reinhold for issues regarding the shoulder.