ANever done it. It looks like buttercream. I would do a coat in chocolate, chill well, then a thin coat of white/ivory or whatever colour your top coat will be. Chill again, really well. Somehow remove the top coat where you want the distressed look. I would try a brand new sheet of fine sand paper to be honest. Then give the cake a good brushing down with a dry pastry brush to remove any dust. I really like the look, never seen it before!
AI'm a novice but I would think the easiest thing to do would be to use fondant and a dark luster dust.....maybe put some lightly on a cloth/paper towel and shake excess off then rub over most of surface? As for the darker corners maybe do those first with a food safe marker or paint then buff with the luster dust cloth to make the lines not so "sharp" would prob work on buttercream if you got it firm enough with chilling....just my opinion!!! Experiment :)
ALooking more closely, instead of drawing the darker parts... sponge the edible paint on! I would start lightly since its way Easyer to go darker then it is to lighten it up