The writer of this article apparently watched Wall Street, and has not done much research on PE since.
Private equity is a net positive for workers, because private equity typically buys smaller companies or those that are struggling and would otherwise not have access to capital. Paying down debt is one aspect of how PE firms make money, but the much more important way is making the companies more valuable. This means investing in businesses, making better products, and making them more efficient so they can grow, which typically results in hiring more people. Countries that have smaller PE industries relative to the size of their economy typically have slower growth and more unemployment.
The existence of PE also encourages companies to invest in themselves. A family run business is more likely to update its stores, factories and technology if it thinks that will make the company more valuable to a future acquirer.
Finally, PE companies have much, much, much (you can keep adding "much's" for a while) more employee ownership than family owned businesses. Employee's also have much more leverage against PE owners in negotiations over compensation with PE firms, who are "on the clock" as soon as they invest and are very sensitive to labor disruption, than they do with family businesses, which are usually run for cash flow for the founder's heirs and often view employees as disposable. PE firms are happy to back employee buyouts of businesses if the price is right. PE firms do not have a political agenda, they are completely coin operated, which is a good thing for employees.