Here are some problems I see with the argument made by the video:
Can we also not forget that there have been a lot of wrong theories in Psychology. For example, Egas Moniz won a Nobel Price for Lobotomy when they thought it helped cure specific mental illnesses, when in reality they caused brain damage in thousands of people. The point here is, Psychology is still a relatively young field, with Typology not being the main focus. There isn't enough research to prove or disprove MBTI, therefor it seems silly to me to completely deny it—especially just because a "professional says so".
It's nice that they took one line out of Jungs book, but they also forgot to mention or at least understand that Jung wasn't talking about Introversion and Extroversion in the same sense that we do when we talk about being "drained" or "energized" by social interaction. Jungs focus was on how people are either drawn to interact with the object (extroversion) or pull meaning from the object (introversion). They also forgot a major piece of Jungs theory, which is a level of mental conciseness with certain functions. The reason why Jung said that it can't be predefined, is because he believed people developed differently and eventually encompassed their type as a whole when healthy.
The forer effect was just tossed in their video to support their faulty argument. All of the descriptions of the types would have to be general for everybody to see themselves in them, which isn't the case. You'll find that most people who can't find their type tend to limit it down to a select few. While the MBTI descriptions aren't the best, they're a lot more specific than Horoscopes.