Hmm, well... the base is peat/ coco with some perlite... so that part is a good start to having a lightweight mix that can achieve proper capillary action to wick water up. However, the thing that would concern me about this mix is that they imply it's pretty hot stuff with the way they want you to use it. They don't want you to plant directly into the mix, but place it at the bottom of more inert mix. I assume this is in order to avoid burning the plants and to get a slow release of nutes.
This could be a problem in a SIPS for a couple reasons. If the mix is too dense then it may become too saturated because it will be all down near the reservoir and this may prevent water from properly wicking up into the rest of the grow medium. Stuff like worm castings, guano and humus can potentially make the medium too dense and therefore too wet. You could try to put a lot more perlite into it to lighten it up. When I use peat moss I usually amend it with 40% perlite. With a dense mix you might want to go higher than this with perlite.
The other issue is having water percolate up through this hot mix could cause young plants to get too much nutrients early and then not enough later in the grow. But, I'm speculating on this one. The way I apply my fertilizer is actually at the top of the system. I carve trenches along the top outside edges of the bucket grow medium and pour slow release organic powdered fertilizer into the trenches and then cover it over with peat. The water wicks up and slowly activates the nutrients over a long time rather than the powder nutrients getting too wet if it was mixed lower in the SIPS container. Roots radiate out to the trenches of fertilizer as the plant gets larger and need more nutrients. In your case, you could try to use the kind soil around the perimeter of the container in the ratio they suggest and then fill the rest of the container with the inert medium. That way your plant wouldn't be directly in the kind soil, but the denser kind soil wouldn't be at the bottom of the SIPS. You might get a slow release of nutrients similar to the trench technique without affecting water wicking capability.
One other thing I do in peat medium is add a bit of dolomite lime, usually 1-2 tbsp per gallon of medium to provide some calcium throughout the grow. I have also had to supplement with some Cal-Mag in the res later in the grow... especially for tomatoes and cannabis. But, the kind mix might have enough calcium.