From anecdotal experience - the training plan he describes is something I did when I started out mountainbiking and ran straight into a probably best coach in vicinity.
My training program was a lot like the one described in the article - It was longer, but I was too lazy to do all of it - so I landed right where he suggests 3-4 times lifting weights a week. And boy did I get strong. But then I started fiddling out with trendy programs and fuxxored it all. :)
I guess that not using machines wont make such a difference, its more the training regime (reps, measuring your maximum, doing the pyramid). It's just that they are unnecessary.
So there are 3 things I have learned about fitness:
1. Your basic training / off season training should be exactly as described in this article.
2. Most people work out waaay too much.
3. If you are serious about your sport: do interval training twice a week (max).
That's it - that's all are there is. Everything else you can do your sport or whatever.