In the study you cite, and in many other sources, the bottom line is basically this, "Endurance performance of the longest durations was enhanced most by intervals of maximal and supramaximal intensities". If you look at the RBR link I gave above, they suggest "do intervals on the road or on a trainer. There are 2 basic types for this discussion: short intense efforts of 30 seconds or less, long intense efforts of 2 minutes or more".
The key is the intensity; there is near-universal agreement on that. I think this leaves two questions:
1. Does it matter how the "intensity" is achieved? Cycling intervals or long squat sets with weights at 60-70% of 1 rep max? If the cardio and respiratory systems are stressed to the same level how does the body know the difference?
2. The bigger puzzle to me is WHY short intense efforts translate into endurance improvements. I agree about the importance of VO2 Max, but that's a whole body measurement, and I think we should also look for explanations at the cell level. The puzzle is that short intense efforts use different energy production mechanisms than efforts that last minutes/hours, so how does an improvement translate across time scales that vary by factors of >100? Okay, VO2 max is improved, but why?
Classic heavy weight training, as in single rep max, may not do much for endurance performance. However, if you do any sort of a program that includes sets that are >30 seconds long, the training effect is the same as an intense effort on a bike. It feels the same when I'm done, my breathing is the same, and it looks the same on my HRM. One example is the 5/3/1 program of Dave Wendler. The last set is "to exhaustion" and that definitely gets into the >30 second regime and sometimes into the 2 minutes.
I'm aware that this is a near-religious point of contention and has been debated to death. People I respect and read (Lon Kilgore, Mark Rippetoe) are on one side of this issue, while others I read and respect (Andy Coggan) are on the other, with still others (Joe Friel, Chris Carmichael) sort of in the middle. So, I'm just posing questions, not taking a religious position. Much of the controversy may come from the studies that purport to "prove" one conclusion or the other. In --untrained-- or slightly trained individuals, I'd suggest there is a lot of cross-over in training effect regardless of what that training is. At an elite level, it may be different. Since my cycling level isn't in that range
, I can't comment.