The example given sounds more like simple age discrimination to me. The company can't actually fire him that close to retirement age without making it obvious, so theywork in little ways to make his life miserable.
Most of the folks I hear whining about "quiet quitting" seem to be complaining about people doing their jobs for the number of hours they've agreed up front to be paid to do them and not pitch in extra unpaid labor for free. Wouldn't then the proper analogous "quiet firing" be companies that don't hand out extra money and incentives beyond the amount they've agreed up front to pay? Wouldn't "silent quitting" and "silent firing" often describe the exact same scenario, just from different perspectives?
Mathematicians practice absolute freedom. -- Henry Adams