Why does the ink on my whiteboard move?
This is a wild guess, so I am open to criticism.

Brownian motion could explain this phenomena. 


Water was on the board, so it is possible a film of water condensed on the board some time in the night.  This means the humidity was high while the board was still relatively cool. This film may have allowed the oil particles to suspend. 
The ink bound tighter to itself than the non-porous glass board, and the ink itself may be buoyant in water.
The ink binding to itself explains why the letters stayed semi-intact instead of diffusing into a mess.
The water molecules are moving constantly which would allow the bigger particles, which in this case would be the letters, to do the random walk characteristic of Brownian motion.
(As a note the random walk characteristic of Brownian motion tends in the direction of gravity.)
The diffusion coefficient of the letters would be temperature dependent, so the temperature in the room may have briefly spiked just warm enough for the oil to diffuse some then it came back down so the ink did not run completely off the board.