Why did a use a vaccum cleaner motor?

Because they are constructed for high RPM's. A DC motor/generator would fly apart at 6500rpm's. The universal motor is made for 20K rpm's.

Why 6500rpm's?

The tiny weed-eater engine with it's 25cc volume generates the 1KW power at that high rpm. Lower and it doesn't have any horsepower.

It is a fly-by-wire system so the trottlegrip is just a potentiometer and an Arduino is controlling the engine throttle and the pump rpm's

The Li-ION pack supports the generator with power and delivering a total of 2KW to the pump thrusters.