The current understanding of waves on a liquid surface is attributed to a clear boundary between two fluids with a density difference and a velocity gradient. Gravity plays no role in this.
Two fluids with a density difference and a velocity gradient usually have a common force acting upon them, e.g. gravity, which enforces so-said interface. Perturbations to the average interface are restored via this force, and these perturbations are called gravity waves.
KH Instabilities give rise to gravity waves.