HDMI has a 5V power rail (your adapter isn't passive, it's just parasitic on that rail). I'm guessing that this old hardware isn't equipped with diodes everywhere, and the fan 5V is connected directly to the PCIe 5V rail, and the card is also not shielded and so the 5V rail ends up directly connected to the monitor.
If i was to guess I'd say that the adapter itself also has a part in this. I think it is sending back power when it shouldn't.