These are my tires, Falken ZIEX ZE 914 (Size 175/50 R15 75H) mounted left and right.
They are clearly asymmetric and have a distinct outside edge, but are not directional - there's no direction indicator and you can't buy right/left versions.
Now I'm wondering why the treads are not symmetric between the left and right tire.
It is usually said that mounting a directional tire against its direction causes a loss of performance, which is small on dry roads, but increases on wet / very wet roads. I'd say it would be no good idea to mount directional tires correctly on one side and against their direction on the other (You'd need four wheels with same direction for this)
So, is the effect so small that it doesn't matter for these tires since they don't have a V-shaped tread?