Those two buttons on the left are intended to be read using an analog to digital converter. They don't provide a simple digital signal.
There's probably a pull up resistor on another circuit board.
Something like this:
simulate this circuit – Schematic created using CircuitLab
The value of R4 is probably wrong - it is just a place holder value since I don't know what the rest of the circuit looks like.
The ADC can read four values. Each combination will be represented by a different voltage. Using the given resistor values and my assumed value for R4, you would get the following:
- SW1 and SW2 open - 4.7V
- SW1 closed, SW2 open - 1.38V
- SW1 open, SW2 closed - 3.4V
- SW1 and SW2 closed - 1.2
There is a fifth condition: When the button PCB is disconnected from the ADC PCB, then the ADC will see the full 5V. The ADC side might use that to detect when the button PCB is disconnected - or maybe not.
The advantage is that you get two buttons for one pin. The disadvantage is that you need an ADC to tell which button was pressed.
The circuit may have been intended to pull the ADC input up. That depends on whether pin 7 is ground or a voltage source.
The buttons on the right appear to be in parallel. You cannot tell which was pressed. Electrically, they are the same. There may have been one large button with two contact pads there.