I was a runner for many years and I've never encountered this idea that running makes the body store fat. His before and after pictures don't tell the whole story. His puffiness is most likely extra stored glycogen and water due to tapering for the marathon. His muscle gain is certainly due to reduced mileage allowing him to regain his natural level of muscle.
Claiming sprinting builds muscle by looking at sprinters is misleading. Sprinting self selects for a muscular, powerful build just as distance running selects for the thin and lean.
His diet after his long runs shows little knowledge of refuel after near depletion of glycogen.
Also, the claims that a few minutes of high intensity work is misleading. You can't jump into a sprinting workout without a solid warmup and cooldown which can add up to a fair amount of running which is not accounted for.
"To give anything less than your best is to sacrifice the Gift."