@michallis Yes, exactly. Making a shadow plane used to be very complicated and required messing around in the compositor, but they added an Easy Button in Blender 2.79b (I think). In the plane’s Properties in the Object tab down at the bottom in the Cycles Settings section there’s a Shadow Catcher tick box. Tick it and you’re done; just the shadow will render over any background.
I should have removed the plane before uploading to Sketchfab though, because it seems Sketchfab just considers it a normal plane and renders it, heh.