If you squat like the video you mentioned, you'll develop knee problems pretty fast. So please, don't perform it like that
As others have mentioned, squat is an awesome body-weight exercise that mainly works the legs. However, there are variations of squats that can work the entire body.
For example, it can be used as a form of cardio exercise by increasing the speed of the repetition. That will increase your heart and lungs' endurance.
You can also include jumping to it. Instead of standing up from the squat position, you jump into the air as high as you can. That increases the intensity and works your heart and lungs as well (P90X participants should already be aware of that modification).
Of course, it can also be modified into a burpee by including planking and jumping to the routine.
Lastly, you can include barbell and weights with it; that works your entire body as well.
Hope this helps.