The problem I see with these double versus bolt action speed tests, is that they are always conducted and filmed under controlled conditions at non animal, read dangerous animal, targets. It is a ready set go a bit like a timed quick draw.

From what I have observed on several videos hunting elephant and buffalo, the double is certainly very quick for the first two shots, where two quick shots are used from the same position but after the first shot with a double or bolt gun, if the hunter needs to change position for a second shot e.g. move around bush to get a clear view, then the bolt can be reloaded on the move so neither gun type has an advantage.

The disadvantage I've observed with the double comes when both barrels have been emptied and then the hunter is physically pulled or strongly urged by the PH to change position or run away from other agitated animals, then the double user either doesn't reload until he has re-positioned or got out of harms way, or hung back and tried to reload before moving off.
The bolt gun wins hands down as it can be reloaded from the magazine from almost any position to prevent snagging on brush and all the while during full tilt running if need be while the hunter can keep his eyes on where he is running and avoid trips and falls and of course on what the game and PH is doing.

A broken open gun is a pain to reload when moving around and running let alone when running through brush and over uneven ground. Next time when out with your SxS or O/U shotgun, try reloading on the run and then try the same with your semi-auto, not for the speed of shots, but just for the shear ease of having a magazine full and also the ease of recharging the magazine on the trot.

I have observed in videos even the most experienced hunters and users of doubles either not reloading when on the run thus have an empty gun and relying on the PH to provide quick follow up shots with his bolt gun or fluffing around trying to eject empties, pluck two more cartridges from the belt and recharge their double all the while being urged by the PH to move.

Yes for two aimed and quick shots on animals the double is in it's glory but comparisons between doubles and bolts as to who can fire the most shots faster under controlled range conditions and uncontrolled field conditions are chalk and cheese.

If i was urged to run by a PH because I've got an ele or buff up my chuff I'd be beating the PH to the tape not pissing around trying to recharge a double.