So if I understand this correctly, Remington set up this test in such a way that the 700 had to pass and the traditional Mauser had to fail. The Remington extractor is designed to slip past the rim of the case, most of the time they will if they are within spec, but the Mauser is not designed to do this. The Mauser claw is designed to have the magazine spring push the head of the cartridge up between the bolt face and and the claw extractor. The claw extractor is not designed to slip over the rim of the case and breakage to the extractor will be the result of improperly cycling with a round placed on the carrier ahead of the bolt. Cycled correctly, there is no way for the Mauser extractor to fail or wear out . . . unlike 3 Remington extractors I've had to replace. Modern Mauser actions apparently are more tolerant if you happen to slam the bolt closed on a round that has not been properly engaged by the bolt, but I don't see that practice as beneficial to either the rifle or the shooter.
If the push feed has an advantage over the CRF, it is that a round can be chambered while the magazine is full. You can't do this with a CRF unless you add the rounds from the bottom through the floorplate. Does this provide any advantage to a hunter armed with a push feed over the CRF? I doubt it. Occasionally one might want a different load in the magazine from what's in the chamber. There is logic to the practice that when hunting African dangerous game the hunter loads a soft is loaded in the chamber while the rest of the magazine is filled with solids. But your magazine will be loaded that way ahead of time. One might imagine that a broadside buff runs directly away at the initial shot, and the follow-up shot must penetrate deeply to stop a very tough animal from escaping. In this scenario you would not be dropping rounds from your pocket in front of the bolt, and by the time you've fired a third shot from your 3 shot capacity bolt gun, you've either succeeded or failed, there was no time for a 4th shot even if you had it. So you reload the magazine and either close the bolt on the top round chambering it or you push the carrier down and close the bolt on an empty chamber with 3 rounds waiting for the next opportunity.
While the advantage of CRF vs push feed could be debated ad nauseam, consider this: spitzer bullets provide the profile that is the easiest to chamber from the magazine. But when hunting dangerous game, particularly at close range, the choice of a spitzer bullet might not be your first or even second choice. That leaves us with a blunt nosed bullet which will tend to deflect from the line of the bore when pushed forward out of the magazine. This is where the CRF actions really shine because the cartridge is held in line with the center of the bore before it can be deflected into the edge of the chamber's opening. In theory, a CRF action can chamber a magazine full of empty cartridges, although the ones that actually can are a happy exception, because if the rifle will cycle empties, it doesn't matter what style or length of bullet you choose, provided it is short enough to fit in the magazine, it will feed.