Web runs done on devices that google recognises as phones (the ones with vertical layout) have been moved over to the mobile category, as there is no discernable difference between the two.

So basically:

Vertical Layout is MOBILE (either website or the app) and must be played with touchscreen.

Horizontal Layout is WEB and you can either play with Mouse/Keyboard or with touchscreen, as it doesn't give any advantage over Mouse/Keyboard considering the input delay that touch screen has (This will give a bit more accessibility for the very few runs of this kind).