The author is essentially saying this: a manager shouldn’t join in complaining about the job/company/personal problems etc. with his/her subordinates, because it sets up false emotional relationship expectations.
You may commiserate with a team member when you both get made redundant, as a healthy example.
When a team of several engineers are all thrown under a bus by a PM, they may commiserate with each other about the workload they find themselves with, as a slightly less healthy (but common) example.
But when you, as a manager, commiserate with the team about the PM throwing you under the bus, you are doing your team and the organisation a disservice, in that you're creating an unhealthy us/them dynamic when doing so, and the other things the article suggests.
it always used to mean some kind of shared negativity though like many words the nuance and original meaning has somewhat drifted.
But I think you're right, he's saying employees are complaining and the boss is providing sympathy.
But the article launches (literally the first sentence) into "As people become managers, it’s quite common for their team members to want to commiserate with them." as though it is just obvious that all managers have some sadness that their team members need to help them through, which is obviously nonsense.
So yes, it's unusual phrasing.
I would consider it commiseration if one were to complain to their coworkers about an HR policy in the hopes of receiving sympathy or agreement about the problems with the policy.