What is the reason? Is it because Dwarfs have higher surface gravity (log g), in turn related to pressure, than Supergiants so there is more contribution from van der Waals and Stark broadening?
Collisional broadening - which includes van der Waals and Stark broadening - is more important in the higher gravity, higher pressure/density atmospheres of dwarf stars (a factor of 100-1000 higher for dwarfs vs giants of the same photospheric temperature).
These collisional effects effectively "truncate" radiative emission and absorption processes, leading to broadening of the frequency response of a line absorption cross-section. That means strong lines have appreciable opacity away from the line centres and means the lines sample a broader range of temperatures in the photosphere.