(H/t The Firearms Blog)
Update (6/30/2015): So my son and I were practicing this the other day with my AKM clone. The magazines were East German steel ribbed magazines. I was not able to grip the magazine and operate the magazine release with my thumb; my son could after some practice. What I resorted to--and as I've seen demonstrated elsewhere--is briskly striking the magazine release with the front top of the new magazine (the divot where it locks on the front tends to act as a bit of hook to help grab the magazine release lever) to knock the old magazine out of the rifle. However, turning it as indicated in the video did noticeably help. My son is left handed, so the reload is even quicker--he only has to turn the rifle on its left side (right side up) for both switching the magazine and charging the rifle.
I suspect (wonder) if it might be easier to grasp the magazine and operate the release with the thumb using polymer magazines that do not have the large rib of the metal magazines.