As well as not smoking, you should also NOT EAT ANYTHING and NOT DRINK ANYTHING while walking. That message on the sign is in Japanese, English, and Chinese. We are all at fault.
Apart from the (small) risk that you may collide with someone and spill your food/drink on them, there is also the practical problem that there are NO PUBLIC RUBBISH BINS. So there is no place to dispose (legally) of your eventually empty food or drink container.
Japan Tourist Tips 