It didn't make sense to me either. When normally I read "commiserate", I think someone is expressing empathy to someone else on their bad fortune. I assumed the employee was sorry something bad happened to their boss.
But I think you're right, he's saying employees are complaining and the boss is providing sympathy.
Yeah, I think it makes more sense when you consider that the former (boss complaining to direct) is something that should seem obviously bad to even non-managers, but handling the reverse situation correctly is also critical. It's confusing because the title is written as if I am the direct report, while the article is written as if I am the manager.
But I think you're right, he's saying employees are complaining and the boss is providing sympathy.