Just MHO:
I've taken a lot of game, big and small, on the run with an open sighted rifle and at close range. Heck, where we deer hunt, if you don't take a shot at a moving deer, you ain't taking a shot! The brush/cattails in the creek bottom is so thick, and they don't come out after opening day.......the only way to fill your tag is to go in and roust them out. I have also done a fair amount of wingshooting, so I think that the idea of "lead" is somewhat "automatic" in my brain when it comes to tracking and hitting a moving target.
Now, I will also say that I have shot at a LOT of (nonliving) moving targets, from clay pigeons to balloons blown by the wind, etc. , so I am comfortable and confident in my abilities to make a fatal hit.
I don't think I would try a running shot with a scope sighted rifle, as I haven't had a whole lot of experience on running game with a scope.....with open sights (such as on my Winchester 94 or M1A1), I can see the target, my sights, the distance, the angle, how fast the critter is moving, etc. and all this gets rapidly processed in my head ....for some reason, with a scope I'm just not able to do this as quickly, and maybe that's because we depend on scopes for "long range" shooting? Just a guess..........
Would I do this (take a running shot) in Africa? Probably not........1.) if I'm hunting Africa, it is a game rich environment, and there is a very good chance that another critter (and possibly a better one) will come along and offer me a better shooting opportunity. 2.) If I have to pay if blood is found, I want to make sure that it is a great hit, not just a good hit. 3.) I've seen the kind of punishment that some of these animals can take and keep on going, so I again want to make every effort to make a good hit. 4.) Going back to #1, there really isn't any need to. Unlike here in the states, there is no "closed" season, you are most likely there for at least a week (as opposed to a day or two maybe back at home), etc.
I will say that if you are going to attempt shots at running game, build your confidence on nonliving moving targets, such as the tire mentioned above, balloons blown by the wind, targets on a rail system , etc. I do NOT believe that just because an animal is not considered a "trophy" or a "game" animal (i.e. coyote, raccoon, rat, etc) that is should be thought of as something for "target" practice.......I think if you are going to kill a living critter, it deserves the same considerations as one would give a bull elk or monster kudu with re: a humane kill.......but that is just my opinion.
Just my thoughts............yours may vary.