Thats a bad deal. The
VIA (a connection through the PCB to another layer/side) is gone completely. This via in particular is important because it is the last spot to get the A button before the MCU. So with those being bad, the only way to fix it is to solder directly to the MCU. This will require excellent soldering skills to correct. I have circled the spots you need to connect.
The buttons are CG or common ground. So the A and B spots are live inputs, so if you touch them together you are causing a short. The A spot (top of the button pad or anywhere along the trace/via) connects to ground (the bottom of the button pad or any ground spot ont he controller, hence common ground) to activate