It is instinctive for cats to cover up any food that they have not eaten, to hide it from other animals who might eat it. What he is doing is attempting to cover it up. Outside, they would have some success in covering it with earth, etc. using their paws in the manner you describe. Mine does it to the dog's dinner as well.
Because he is a domesticated cat instinctive behaviour like that will not happen all the time. Sometimes my cat will cover his poo, on other occasions he will just not bother!
I have read somewhere that cats secrete a scent from their pads when they claw carpet trees etc maybe when you put new paper down he's doing that, it is apparently one of the ways in which they mark their teritory?