I'm not sure what he means by no jogging , but I think he means the really long, slow granny jogs that go on for hours. Those of course are not necessary for combat sports. I would however seriously recommend that you
1. run on the track
2. not jog, but be able to RUN, at least 4 miles at a decent pace before you start sprinting
3. I would not recommend tabatas on a tread mill since those are supposed to be max effort runs and I mean, BALLS TO THE WALLS sprints where you do not pace yourself. The tread mill defeats the purpose by having a set pace which maybe way under your limit and it is also mechanically powered which is different from running on the track. If you do tabatas sprints right, you should feel like dying after the 4th or 5th and if done properly, should even be totally unfinishable on your first try. The reason tabatas work is because regardless of your fitness level you go at your max- without pacing. If you pace yourself, you are doing it wrong.