Very simply rocket fuel burns at a fixed rate that can't be changed after it is made, so most very long range rockets use two types of fuel.
If they used all high power high energy fast burning fuel it would rapidly accelerate but then drag would slow it down... most modern AAMs have at least two rocket fuel types too... the first is fast burning high energy fuel that accelerates the weapon off the missile rail and accelerates it rapidly to high speed. For long range missiles the missile often climbs at the same time, but that high energy fuel burns rapidly so it quickly burns out.... the problem is air... the more power you apply to the rocket the faster it goes but it is not consistent... doubling the engine power does not double the speed and as you get faster and faster for a given aerodynamic shape it actually gets worse... so 10 ton thrust at mach 3, does not mean 20 tons thrust means mach 6... no matter how powerful the engine is there will be a top speed limit so burning high energy rocket fuel all the way to the target means the rocket might reach top speed at 15 seconds in to the flight, but for the rest of the flight it wont accelerate any more, but because the rocket fuel is high energy it also burns much faster so in 50 or 60 seconds it burns out and all of a sudden you have no power and drag starts to decelerate you fairly rapidly unless you compensate with a dive.
A better solution is to use lower energy rocket fuel that burns much much longer but does not have as much energy.
Once the first high energy fuel is burned you don't need to continue using high energy fuel to maintain speed... in fact you just need to counter drag to maintain speed which uses a lot less energy and can burn for several minutes instead of seconds for the high energy fuel.
It has an added bonus for missiles like Iskander, which Kinzhal is based upon because neither missile has large external control surfaces, so it is the lower energy fuel with internal control surfaces that direct the rocket thrust that actually steer the missile on to the target anyway... and it is known that the missile manouvers during its entire flight... it does not have a ballistic path... which proves I am right and you are not.
That was brutal!
A colourful way of stating things, but largely accurate... it is just his opinion and he is totally wrong in this case regarding the workings of the missile in question.