I wouldn't take it that literally. He wrote NW around when he wrote Enter the Kettlebell. He hadn't created the S&S programme yet. Clearly, back then he thought the snatch was superior to the swing, which it is indeed if you are talking about the same (necessarily) light kettlebell. However, you can't do snatches with heavy kettlebells, so, according to a blog article he wrote much more recently, the swing comes out looking quite nice (because you can do it with much heavier kettlebells than you can snatch)!
Having done the NW routine (if we can call it that really) for two months in the summer to good effect, I think I fully understand what he means about the "big pull" having to be included:
NW tones up the body very nicely and imparts brilliant pushing strength. Pullups add grip and lat strength (I don't think other gains are important from pullups as they're covered in the pushups.) The part lacking is the lower back which is SO IMPORTANT for real world strength. If you can't pick up something heavy from the ground then what kind of "strongman" are you???
So, I'm pretty sure that any kind of exercise where you are pulling somthing heavy up from the ground will do: deadlift, swing, clean, snatch, etc...
Based on what I've read here from more experienced people, you can combine the 10X10 swings from S&S with any kind of "big push" exercise to good effect. I considered doing this with the warrior pushups, but instead I decided to not deny myself the benefits of the amazing Turkish Getups, and to therefore drill some one arm pushups as a bonus instead of working through a 5X5 warrior pushup workout as a replacement for the getups. Getups load less weight on you than the pushups, but I think they are much better because they develop multi directional strength.