I like that you include the speed in your description, very useful. Like you said: definitely not a program for your average Joe.
He wants to maintain his base level of strength built for powerlifting but also needs explosive power for his martial arts strikes, good core stability and strength to minimise damage when taking body blows. His gradings have a heavy fitness component requiring a lot of sit ups, push-ups and running. considering sit up are not a good exercise especially as fatigue kicks in and the core weakens to the point of putting the back at high risk of injury. Alternate core exercises are used. There is no point in just replicating the 100 plus push-ups he does in class, fewer push-ups progressed to harder variations keeps the movement specific and is more time efficient and effective when he is already in a fatigued state toward the end of the training session. Rounds of martial arts are mostly anaerobic in nature requiring the training of that energy system with the intervals. Base aerobic capacity is covered with his running each week. unilateral exercises allow for both sides to be worked equally and alternate DB bench require him to maintain good core stability and anti-rotation. Adding the RNT element to the Palloff press adds a new layer of difficulty and muscle activation.
If I remember I will post his alternate day training next week.