Applying a fresh coat of paint over existing non-skid can be done, but..... The main principles behind good paint adhesion are first, the substrate must be clean and secondly, it must be sanded. Due to its rough surface, non-skid is difficult to both clean and sand.
Clean the surface with TSP in warm water with a heavy duty bristle brush. Go over the surface a few times from different directions to ensure surface contact with the bristles. Rinse the surface well with fresh water and allow to dry.
Since the non-skid particles will prevent standard sandpaper from deglossing the surface, use an abrasive pad. Again go over the surface a few times from different direction to ensure that the entire surface is deglossed.
Rinse the surface well and allow to fully dry before painting.