They all have a stationary phase (a solid, or a liquid supported on a solid) and a mobile phase (a liquid or a gas). The mobile phase flows through the stationary phase and carries the components of the mixture with it.
From this, I can infer that the mobile phase would be the solid colour at the bottom of the filter paper, and the water is absorbed by the paper, the colour, which was once solid moves into the stationary phase, in which it is mixed with the water, travelling upward, therefore it can be referred to as a liquid, by becoming a part of the liquid.