I consider plyometrics to be one of the most important types of training. They're high intensity exercises, that encourage rapid movements and shock your central nervous system. They typically involve only your body weight, and a set will last between 10 seconds and a minute. Running/sprinting are the most basic form of plyometrics, but other methods are lunges, step jumps, jumping rope, crocodile walk, burpees, rowing, fast sets of push ups, sit ups, Russian twists, jumping jacks, mountain climbers, etc.
This aspect of training will carry over to Ninja Warrior because you need to move very fast through Stages 1 and 2. All the strength in the world won't save you if you can't power through those obstacles very fast, and have one of the 15 fastest times to advance to the next round.
I do a full cardio/plyometric workout probably 1 day a week, while my other 3 workouts are purely strength training days.