All photosynthesis reaction does need chlorophyll,even in cyanobacteria and algae the difference is the type of chlorophyll ( which depends on available wavelength of light and energy efficiency ) fully parasite plants on the other hand doesn't contain chlorophyll and this force them to live as parasites ( keep in mind that we do have half parasitic plants too,which their problem is lack of roots,they do photosynthesis just like other plants ) plants with non-green leafs does contain chlorophyll in some cases even more than green plants ( in my own experience berberis which is a red to alizarin crimson violet shade has more chlorophyll than a greek lettuce) the other pigments are working as helping energy harvesters in photosynthetic reactions, light/shade controllers or simply a survival strategic materials in answer to climate changes,habitat problems and environmental stresses