Does this thought experiment violate the second law of thermodynamics?

This ratchet-like Maxwell's demon has the same problem as all of the other ones: the door/coil mechanism itself will heat up, and become useless.

Before thinking about this one, think about the simpler scenario where there's just a door, that opens if a fast particle hits it hard enough. Since particles have energy on the order of $kT$, the door must require around that much energy to open. But by the equipartition theorem, once the door itself is at temperature $T$, it will have $kT$ of thermal energy! So after a while the door will be wildly swinging open and shut on its own, and become totally useless.

This machine adds a second stage: now, your particle's $kT$ of kinetic energy goes into making a current in the coil, and the current in the coil opens the door. However, thermal noise applies to circuits, too; after a while, your coil will reach temperature $T$ and have $kT$ of Johnson noise, giving a randomly fluctuating current. As in the previous case, this will make your door randomly open and close, making the device fail.