I am having two comments on the video:
1. The Alter Rebbe (Rebbe Shneur Zalman of Liadi) never met the Baal Shem Tov but was a student of the Maggid of Mezritch.
2. It wasn’t only the Alter Rebbe spreading Chassidut but there were many more famous students of the Maggid teaching chassidic ideology. One of the most famous ones was Rabbi Elimelech of Lizhansk. Rabbi Elimelech, on the other hand, also had many students who, later on, became very famous. One example is the Chozeh (the Seer) of Lublin.
Not everything is only Chabad and all other chassidic groups actually come from the Chozeh of Lublin (e.g. Satmar and Belz).