I've seen a few examples of using the light path node; looks cool and very useful! Most simply mix two shaders then control the factor via one of the outputs of the light path node. For example a green default cube with red shadows. I can't get this to work! Starting with a default scene, using cycles render engine, I place a plane under the cube then set the plane's shader to a simple white diffuse and the cube's shader up as shown in the demos. The result however is no different than if I just plug the top diffuse shader node directly into the material output. What am I missing? Have watched multiple examples of people explaining the node, all use the same node setup and no-one seems to mention any setting I might have missed.
I'm not sure what tutorials you've been watching, but this setup should work for you. Nothing special - like your attempt, the floor has a white Diffuse BSDF for it's material, and the material for the cube is shown in the graph. If this doesn't work, please let me know (ideally with a screenshot) what you're seeing instead: