The formula for Recoil Energy (Kinetic) is RE = MV.
A 15 lb gun recoiling @30 FPS will give that 210 FtLbs of recoil energy shown for the 8 Bore with 1257 grain "Ball" @ 1500 FPS, matters not whether its rifled, smooth or part of each.
Take a 12ga half that weight (7lbs) & fire 1 oz to 1250 fps & you will get a recoil velocity of about 15 FPS or half that quoted for the above 8 gauge. This 7 lb gun recoiling @ 15 FPS will give a recoil energy of 26 FtLbs or 1/8th that of the 8 bore.
Note that on the weight side of the formula the change is linear while on the velocity side it is proportional to the Square, thus multiplying both factord by 2 gives not 4 times the RE but 8 times.
Of importance though is KE is highly subjective. Of far greater importance to the person firing the shot is the Recoil velocity which in these two cited examples has doubled.
