I compared the routine to the one for the plasma clock project and it's essentially the same. Then I thought to measure the voltage on the T0 and T1 pins. It was floating, and looks like there is no internal pullup resistor inside the chip as I had assumed. I added a couple of pullup resistors to the circuit and the buttons now work as designed. There pullup resistors must have been already present in the plasma clock.

Next to test that pressing both buttons together will cycle the brightness.