Above is a water strider. Notice the dimples in the water where each foot touches the surface of the water.
What's happening here is that the legs of both the water strider and the robot are hydrophobic. The usual explanation involves a diagram much like this one:
To go along with that conceptual drawing, here's a photo of a drop of water on a hydrophobic surface, a leaf:
Those images, however, demonstrate a small drop of water on a larger, flat hydrophobic surface. What happens when you have a large flat surface of water, and a small hydrophobic object? You get something like this:
As you can see, the water is pulling away as much as it can from the hydrophobic material. The amount of force required to displace the water and create that dimple in the water's surface you saw in the first two images matches the weight of the object supported on the surface.
This is essentially the opposite of capillary action, where a hydrophilic material is wetted by the liquid to the point that it draws itself up the sides of the object. Here, the material repels the liquid to the point where the liquid makes a well around the object. In both cases, there's a limit to how much the liquid can be displaced from its flat, "resting" state.
The hydrophobic object is not floating; it does not have a lower density than the water does. If you disturb it so that it is submerged, it will sink. If you put too much weight on the robot for the hydrophobic "foot" surface, it will break through the water's surface, and it will sink.
Despite that, the water strider bot weighs significantly more than a water strider and can still support itself (and it's battery and control chip), steer, and travel quite well across the water's surface. The more surface area of "foot" the robot has, the more force is pushing it out of the water, and therefore the more the robot can weigh.