Why are there holes in the sides of the filter cap? Doesn’t the coffee coming out of them miss being paper-filtered?

The bottom circular rim of the chamber is firmly clamped down on the paper filter when you screw the filter cap onto the bottom of the chamber. Therefore all the coffee that you press down must go through the filter paper. There is a tiny amount of coffee that instead of going straight through the filter and into your mug goes sideways through the filter paper and emerges outside of the chamber in the filter cap. The side holes in the filter cap are there to enable this small amount of coffee to drip down into your mug. If those side holes were not there, some of this coffee would be pushed up and over the rim of the filter cap and then drip outside your mug.