Wouldn't this cake batter be too runny? Would the coffee affect the texture?
Compare that recipe to this very similar one from Ina Garten (complete with handy video) Chocolate Buttermilk Cake. Watch her pour. No question, that is a wet batter. Apparently it works fine, Ina's recipe is very highly rated.

Both recipes use volumetric measurements (ugh), so I'll use cups.

Ina's recipe (sugar is wet (sort of), subject for another question) - Wet ingredients (2 + 1 + .5 + 1 + .5 (eggs) = 5 cups wet to 2.5 cups dry (flour plus cocoa) 5/2.5 = 2

Your recipe: Wet ingredients (2.5 + 1.5 + 1.33 + 1.5 + .75 (egg) =  7.58 cups wet to 4 cups dry (flour plus cocoa) 7.58/4 = 1.9

So they're very close, Ina's actually a bit "wetter". 

I am not aware of anything special the coffee would do to the baking chemistry here. It's got some acid, but I don't think that is relevant. As far as the "wetness" of the batter, it's the same as water as far as I know. The temperature might help dissolve the sugar, but that would be a minor thing at best.