Using a Bloopy Thing to print on all sorts of materials is called “Pad Printing” or tampography. Here’s a Big Bloopy Thing printing a very beautiful pattern onto a bowl (and here’s two of them going at the same time.)

You can use the same technique on all sorts of things: plastic bins, pens, keychains, golf balls, pills. The silicone/bloop conforms to the shape of the object to print on rather easily.

Quality Logo Products has a quick explanation: