tiny quantity of egg in a cookie
One thing to keep in mind is that they are in the "Contains 2% or less" section, which means they are exempt from the "descending order requirement". So all we know is that they are less that 2% of the total weight. I just looked at one typical chocolate chip cookie recipe that gave weights in grams, and it was 8% eggs by weight (114 grams out of 1419). So 2% isn't totally off the map - it probably is still enough to provide some binding and richness.