Since you have a Pi3 and a Fritz.Box you might want to try the WPS feature. Just boot the Pi and simultaneously activate the WPS on your Fritz.Box.
Of course, if you want a LAN-connection, that should usually work easily, too. All your steps seem correct and the LAN port blinking also indicates an active connection.
Have you updated the system to 2.37? Have you tried typing http://max2play/ into some devices connected to your local network?