Based on looking at your pictures it looks as if the pcb has been done for the actual analogue joystick component. The pictured one on the right is already soldered to a breakout board. The board you have had designed is for the 'raw' joystick, not one already soldered to its own pcb.
Its the same for the tactile switches. The ones on your screencap are on their own pcbs already and the designed one has the holes for the actual component. It looks like the pcb is correct, you just need to source the actual components