You're completely leaving out sport-specific conditioning. The OP was talking about fitness FOR fighting/competition I believe. These are only measures of general conditioning. I know plenty of people in the kinesiology department that have higher VO2maxs, MLSS, 1RMs, flexibility, etc, that no nothing about how to move with another person.
To my knowledge research hasn't been done on fitness characteristics of good IMA practitioners (but I'm working on it!).
Sure, there are slight differences. But this does not really negate my point. The most important point is that "fitness" of an IMA practitioner cannot be something completely different than that of a MMA athlete or of a tennis player. Fitness is fitness. There will be naturally differences in the distribution, e.g. one may have better active kicking flexibility (Taekwondo) or another better grip strength (Judo). The training for fitness is on a foundation level the same.
Does your sport require high max power outputs? -> focus on intramuscular coordination training.
Lacking in absolute power? Then increase your muscle mass - >hypertrophy training
Does your sport require rapid alterations from aerobic to anaerobic endurance and intensity levels? (e.g. MMA rounds)-> Competition akin endurance methods, Fartlek, HIIT
etc.
Does your "sport" require your postural stability to adapt rapidly to outer disturbances? (e.g. Pushing Hands) Use reactive stability training methods.
Which attribute is needed in your sport? Choose best method to enhance it.
The tactical/technical skills are then still something different. But they are not the same as motor fitness.
(e.g. Jack Mace)