That's the strangest definition of middle class I've ever seen. The more common definition is something like:
Upper class (top 1%, Ivy league educated, heirs, celebrities, household income >$500,000, multi-millionaires and billionaires)
Upper middle class (next 15%, highly educated, professionals and upper management with a high degree of autonomy, household income >$100,000, good amount of assets, generally on track to be millionaires)
Lower middle class (next 30%, college educated or skilled labor, white collar technical or mid-level management some some autonomy, household income >$50,000, little assets outside 401k and the home)
Working class (next 40%, high school or some college or semi-skilled, blue and pink collar jobs in service, clerical, and labor with little autonomy, household income >$30,000, no assets.
Working poor (some high school, unskilled McJobs paying little more than minimum wage)
Poor (At most limited participation in the workforce, completely dependent on government transfers and charity)
There's a lot of overlap there. For example, a family relying on the income of a janitor making $10 an hour would be poor while if the wife also worked at a gas station they'd be working poor. A lawyer working in public interest sector (starting salary of 30k) would usually be considered either upper or lower middle class rather than working class (as their income would indicate) because they are highly educated and have a great deal of autonomy.