There is a difference between middle class and middle income. What's being described in the video are measures of income not measures of class. Income is one of three factors of class, however, income alone does not determine class.
Class is determined by:
Cash: economic resources, especially income, wealth, freedom from poverty
Credentials: educational achievements and qualifications, occupational status
Culture: attitudes, mindset, behavior, self-definition
With respect to the "culture" factor, middle class families place a high priority on education, marriage, in-tact family units, ambition, hard work, etc. In addition to the income and credentials, if these are not values that are a high priority for you, then most likely you're not middle class.
The video gets it right by saying class, for the most part, is hereditary. Your family, community/neighborhood, and network typically determines your class.
If you take someone like Lil Durk whose net worth could be somewhere around $10 million (just a hypothetical), his income alone puts him in the high or upper income earner class. However, if he does not subscribe to the broader values of the upper middle/upper class (which are typically hereditary and are acquired through family/community/network), then he is not. He is lower class/high income.
Black folks that are truly middle class, are typically those that descend from the historic black bourgeoisie, or those that come from professional families that took advantage of the gains made by the Civil Rights movement.
Most black people are working class in terms of credentials and culture even though their income may vary, whether they may be high, middle, or low income earners.
The 1980's was like a 2nd Reconstruction era for the black middle class. This is when the gains from the Civil Rights era were being materialized. If your family did not see any gains during this decade and you had family members affected by the crack epidemic and gang culture, then you're most likely not middle class.
I had not even heard of the crack epidemic and did not know the extent to which it affected many black families, until I got to college in the mid 00's. And it was from an argument I had with the entire membership at a BSU meeting, where members were telling me of the devastating impact of the crack epidemic and how it affected all black families of which I had to argue that it had not. Never even heard of it up until that point and hadn't known any black families within my community and network that were affected by it.
My grandparents and their siblings were taking chauffeured limos just to go to the grocery store during the 80's and 90's (dead serious). That's how unaffected we were.