Hello! Here is your random engineer: You have to connect both trap doors to the same side of the turbine. Otherwise your generator has a great chance to get blocked by users.
Otherwise the concept looks good. If we find a way to get the Linux guys out and make them able to walk a slight incline without collapsing this should work.
Tbh any turbine likely has the potential to be blocked, if two come along at once, making one become trapped between the turbine blade and the wall.
For maximal efficiency, I would suggest a spring-loaded ring of rollers inside a solid metal ring, conforming to the shape of passing Linux users. The dynamos would need to be calibrated such that the stiction of passing users is enough to slow their fall to match the current flow rate of entering users (n.b. is this doable? If not may need to use the spring pressure for this) to ensure maximal energy extraction for available user flow.
To address the blocking issue, i propose a vibrating (and cushioned) funnel to make sure that the linux users get to the turbine in single file. this keeps the system simpler and helps the linux users pass more easily, because it adheres to the UNIX philosophy of doing just one thing, which works as a lubricant.
energy would be used by the Linux guys. That energy is probably equal or less than what the turbine produces. That makes it not a perpetual motion machine. It is free energy for the owner though as long as the speakers don't consume too much energy as the Linux guys will come and for free to no cost of the owner