I have an auto door and have watched it close many times. It is so slow that any chicken in its right mind would easily be able to escape it. Unless the cable to raise/lower the door broke.
I’m SO SORRY this happened to you & your rooster.
What is th brand that has a safety?That door looks like it is powered by an electric actuator with no safety devices to stop it if there's an obstruction (like your rooster) in the opening. Those actuators can be very powerful and will just keep trying to close the door with something under it, as you found with your rooster.