I've found through playing soccer, running track/cross-country, wrestling, kung-fu, and bike-racing, that mental training makes a bigger difference in performance than physical fitness. It's in addition to the fitness-parity that's a given. In any event, you're gonna have a close spread of +/- 10-15% fitness or so and what differentiates the winners from the rest is their mental state and strategy.
From what I can gather from that website, they cover one aspect of mental training: relaxation and serenity, positive attitudes. This is similar to yoga, pilates and meditation in that it harmonizes your mind with your body and allows you optimal control and lets you extract maximum physical performance from it.
The other part of mental training is skills and strategy. The only way to achieve this is through experience and practice. Bike-handing exercises through cone courses, practicing maximum-braking, bunny-hopping, shifting/turning/braking simultaneously, etc. Learning pack-riding and maneuvering skills, racing tactics, pushing & shoving, team strategies, etc.
The final part of mental training combines all the above with visualization and rehearsal of scenarios. You practice this off and on the bike, before, during and after the event. You'll mentally visualize racing scenarios like starting breaks, chasing breaks, hiding in the pack, watching out for the stronger riders to follow, setting up for primes and sprints, working with teammates, etc. You'll then execute this plan in real-life and watch how it unfolds, make mental notes on how it differs from your ideal scenario. Then afterwards, you'll go back and revise your plans and make new tactics and strategies. Visualize and plan it, rehearsh it, execute it, and revise again and again...
This final stage of working it all together is very similar to the think-plan-execute-revise scenarios that's prevalent in many development philosophies you encounter in other areas of life such as business or relationships. Programs like Covey or Carnegie or Robbins, Insight, etc. The power and strength comes from within.