I've found that the way they honor this guarantee is that you simply return it for the reason "Did not arrive on time" and you get a refund.

I've done it once because it didn't arrive on Friday, wouldn't come until Monday, and I wanted it for that weekend so I just went out and bought it and returned what Amazon delivered Monday. I felt kinda guilty but when it came Monday it looked like it was run over by a truck anyways, as in, had actual tire tracks on it.