How did Einstein or whoever figure out that gravity waves travel at light speed?

When a fluid element is displaced on an interface or internally to a region with a different density, gravity tries to restore the parcel toward equilibrium resulting in an oscillation about the equilibrium state or wave orbit. Gravity waves on an air?sea interface are called surface gravity waves or surface waves while internal gravity waves are called internal waves. Wind-generated waves on the water surface are examples of gravity waves, and tsunamis and ocean tides are others.
--- That is a gravity wave.

Gravity itself is simply a force generated by anything that has a mass.

The waves haven't been observed.  Their existence and speed are predicted by theory, though.

The best theory we have for gravity these days is general relativity.  General relativity includes an equation that governs the gravitational field, and it turns out that this equation has solutions that look like waves and move at the usual speed of light.