Huh I never thought about it that way. My questions would be, since fermentation is exothermic, how many calories are lost to heat? (Edit: Looks like TexLaw beat me to this as I was typing)
Another route to go would be this: I did some googling and found that 1 gram of alcohol has 7 calories. 12 oz of 8% abv cider yields this:
12 oz * 8% = .96 oz of alcohol = 27.2 grams of alcohol
27.2 g * 7 cal/g = 190.5 calories
So, since it ferments out so dry, my guess would be that the only calories in apfelwein come from the alcohol, which would mean a 12 oz bottle has around 190 calories. This is the absolute minimum it could have, though. There is probably a small amount of carbs, which may boost the caloric content up a bit (10-20cal?).
EDIT: Ugh just realized that google, which I used to convert units, may have converted fluid oz to grams, which doesn't make sense. The finals answer seems reasonable, though, so maybe it's not that off. You could fix it if someone found the molar mass of alcohol, which I think would let you go from volume to mass... maybe. It's been awhile since high school chem.