I am certainly no expert on running shots on game at long range or any range for that matter but I would say there are not alot of guys out there that have studied and hunted whitetail deer any harder or more seriously then I have. This is my problem with the question posed.
A. IS it possible to make these shots, possible yes, likely NO.
B. To make these shots, the shooter has to be perfect, not only that the target animal must be traveling in a consistant direction, consistant speed and remain at a consistant elevation. In my experience, a whitetail deer WILL Rarely do any of these. That very common "Whitetail Bounce" would cause severe problems making consistant shots. This is when a whitetail is running smoothly and then for no apparent reason, takes a 20 foot bound and then starts running smooth again, then another bound, very inconsistant and IMPOSSIBLE to predict.
C. Most that talk about such feets may have done this once, maybe even twice but then believe they can do it all the time, FOOLISH at best. Generally those that talk all the time DO VERY LITTLE, especially when they are flapping their jaws on a web site with no accountability of any kind, makes super marksmen out of alot of very inexperienced big game hunters.
In real life the guy probably took a running shot at 300 yards and thought it was 600-700 yards. I would really like to see this guy prove he is this good but not on wild game because I do not believe a word of his claims. THe simple reason why, there is no way that a whitetail will behave predictably enough to make these shots consistantly.
More importantly, do not waste your breath debating this guy because its hard to debate fantasy and I am sure about 99% of these claims are likely covered in pixy dust!!!