This is the strict parent, who disciplines their children (or other children) publicly. Although the name may sound confusing, it’s an ironic reference to the the contrasts between how actual penguin mothers are incredibly loving and caring, versus the public disciplinarian.
This parent, in the middle of their children’s game, will charge the field, to yell at a referee, their son, or another kid. This is different from heckling, penguin parents are much more confrontational.