Fair enough, I though it might be a certain style or something. Are running shoes that much more comfortable than say, a nice pair of "dressy" sneakers?
Seen as we're generalizing anyway, I think Japanese tourists tend to wear sneakers, but Chinese tourists do seem to wear running shoes. It's hard to say anything about Europe, because it's more diverse than the US, but I hardly see Europeans wearing actual running shoes as a part of their daily outfit, but they do wear a lot sneakers.
Forget about 'tourists' for a second, but in general amongst younger fashion forward people there is an obsession with cool running/trainers. One only needs to look at the posts on a blog like highsnobiety to see post after post of special edition running shoes - aka: Nike X (famous fashion name) etc.
I will do it sometimes like Kappelan has, but often it's to do with comfort and sometimes it's the Sportcoat that is the afterthought, not the shoes. Or when traveling, if I'm taking a Sportcoat, it's much easier to wear it than pack it and if I happenf to be wearing jeans and sneakers, so be it.