If the chap leading this research says ""honestly, I just don't know how that happens...I think it's a small miracle it happened at all." Then he is either the most honest scientist ever or he knows that his findings are shaky and is genuinely clueless. Mostly these types are pretty keen to hail their findings as the biggest thing since vaccinations. This is going to take years of work in mice before he knows exactly what's going on, then more years to make sure it's safe and actually works before human testing is even suggested.
The report seems to suggest that the effects are a) aerobic and b) muscular in nature. This is a funny combination because one would normally expect either aerobic stuff to happen in the cardiovascular system, whilst things that build muscle mass and strength are largely anaerobic. The increase in endurance suggests to me that the drug acts to decrease the rate at which muscles tire, so that could be a few things. An increase in the number of energy producing elements (mitochondria) in the muscle cells would probably not help much without a similar increase in sugar and oxygen supply, which would mean an improved blood supply to the muscles. A drug that does both of these things without any other effect in the body does not seem likely. The physical movement of a muscle fibre is determined by calcium ions, the lack or depletion of which is what causes cramp and muscle stiffness. A way to increase the recycling of calcium would increase endurance, by holding off fatigue for a while. This would be similar to the gradual effects experienced by, say, someone training for a marathon.
Crucially, though, (bearing in mind that the actual drug is most likely none of these things) the human body, particularly under stress, is horrendously complicated and I am quite skeptical about the ability of one drug to dramatically increase endurance. The act of exercise requires the cooperation of hundreds of different pathways and chain reactions, all controlled by wildly different elements. Even were it able to, the benefits of increased muscular endurance would only be apparent in someone with already developed cardiovascular endurance, muscular mass, physical fitness etc. associated with being generally fit and doing exercise in the first place.