The button that is hooked up to the lowest resistance is what gets reported. If you check out the schematic, you’ll see that all the switches are connected directly on the right side.
So let’s say you press the Left button at first, which causes the voltage divider to end up running through the 330 Ohm, 620 Ohm and 1 kOhm resistors in series, or 1950 Ohm total.
Now let’s say you also press the Select button. At first you might think this adds the 3.3 kOhm resistor into the mix. However, because the switches are all connected directly on the other side, you’ve basically got another resistor of 0 (zero) Ohm in parallel to it, making the combined resistance pretty much 0 Ohm, and you’re left with the 1950 Ohm.
If instead you add the Down button, the direct connection between the left and the down buttons ends up in parallel to the 1 kOhm resistor, removing that, and thus leaving you only with the 330 Ohm and 620 Ohm resistors, same as if you had only pressed the Down button.
If instead of the direct connections there had been further resistors (carefully selected) on the right side of the switches, then it could have been made to detect multiple buttons being pressed at once as well, though the error margin in the analog read would also get to be much lower. Fun exercise: figure out the optimal resistor values (let’s stick to the E12 range) to use for such a situation. Aspirin’s on me :)