Hi TS, I can't tell you how to train for other martial arts but I box. So I'm just gonna tell you what is recommended for boxers. (Not that I follow everything, because I'm lazy )

Please remember that boxers train specifically for that 3 mins round.
Cardio
Running

• At amateur level, 3 times a week 10km runs (I only manage 5km 3 times a week)
• Each run is divided into sections. First section is plain running for about 3km.
• Next section is 3 mins fast run (not quite a sprint yet) and then 2 mins of shadowboxing while jogging
• The final section is sprinting to the finish

Misc

• Squat jumps
• Burpees
• Lunges
• Leg raises
• Jump punches
• Jump twists
• Obstacle course type tyre exercise (i have no idea what its called)

*note that all these misc exercises are done while running. This run is separate from the 10km recommended runs

Martial arts specific
This you'll have to fill in yourself because it depends on the martial art you practice. But it should be about 4-6 hours a week.

Strength
Old school boxing coaches don't agree with weight training. They say it makes you slow. I'm not sure but I still do weights because power is important

I think you'd better ask the weights guru-s here for weight exercises that focus on explosive power and endurance, not strength. Since boxing is core and footwork centric, I mainly do core exercises.

Uh, I forgot to mention. During the 10km runs, the 3mins fast run 2 mins shadow boxing is done in a cycle. So 3-2-3-2-3-2 until the final phase where you sprint.

Also, even with all these, I'm still a fatty because I drink and smoke (too much). So diet is very important. I lost 13kg in 2 months when I regulated my food and drink. But then I started again. IMHO diet is the most difficult part.

Truth. You, sir, know what you are talking about.