I'm guessing your program is more of a mass/bodybuilder program...
Does your instructor only train you in technique? I did a sample KM class and we were doing fitness drills for most of the class.
Swede's right pointing you toward speed and endurance. If you want to train in a regular gym, there are good OLY lifts or even partial OLY lifts that will make you more explosive.
If you do plyometrics, remember that a little goes a long way.... don't work to exhaustion with them. Stop when or before your performance decreases.
A traditional boxing or wrestling training routine is more likely to have what you want. Weights are a great supplement and a bigger stronger guy has an advantage, but arm size doesn't win a fight. Speed, power, tenacity and endurance do...and a willingness to hurt your opponent.
Run the Tough Mudder Sep 6, 2014
"Trust the process."
"Just get stronger, you bunch of knuckleheads."
- Steve Shaw, MaB Founder