I would make two observations:
1) Fast food work is effectively unskilled labor. Small businesses utilize a lot less unskilled labor because they generally start as sole proprietorships and expand when the proprietor's expertise outvalues the proprietor's time. The Cleveland Clinic likely makes the list because "As of 2018, it has over 52,000 employees, a figure that includes over 11,800 nurses and over 3,600 physicians and scientists" - which means they don't outsource custodial and housekeeping. With less than 1/3rd of their employees being healthcare practitioners, 2/3rds of their employees do not enjoy elevated status.
2) The fix is easy: remove healthcare and retirement from private offerings. As a business owner I have a powerful incentive to avoid providing benefits: it already costs me 50 cents to pay them a dollar and when nobody else is providing decent benefits whatever benefits I provide aren't going to enter into salary calculations (because people aren't clever enough to do the math). I'm too small to turn employee insurance into a profit center. Walmart is not. It's easy to hate big companies because they take full advantage of every loophole they've lobbied into the tax code and the corner barbershop couldn't find a lobbyist with a phone book and a flashlight.
It's interesting to me that most of the reactions to this article are actually a reaction to the chart, which was stolen flagrantly from BFX's original post (where it received substantially less notice).