You must have missed the bit in the video where he used an Air Stone with K1. It moved nicely. It starts with the Air line installation at about 17:20.
Indeed I missed that part, it indeed moves nicely. This can only work if the pump pushes the water through the canister. As you can see he has the pump in the tank pushing unfiltered water into the canister inlet. It would be wise first to use a prefilter then, the K1 or Sand bed should be the last stage of biochemical filtration, /nitrification, you don't want any (large) dirt particles collecting in this canister. And also the pump will clog soon if you do not prefilter.
If you would place the pump at the outlet side of the K1 canister the pump will collect all the air bubbles in its impeller housing and lose significant if not all turnover.
So his setup would need a prefilter first then a pump then the K1 canister. I'm not sure how such an upside-down concept setup will work in the long run. It's not ideal.
For about 8 years ago I played a while with K1 and also with a fluidized sandbed filter...
They are all fun to build and have but regarding planted tanks actually a tad over the top. You might not need it, and likely is more than enough.

For a sufficiently planted tank, a decent setup canister filter does the job together with the plants in the tank. All you do extra on top of what is already sufficient enough doesn't make it all any better. Tho it makes it more fancy looking and has a nice learning curve and positive effect on DIY skills and experience and this has value too.
For me personally, it was a nice experiment and experience but in the end, I ditched both concepts after a while simply because of their over-sufficiency and extra bells, whistles and hassle and extra cost while the benefit seen from a filtering perspective only is in your head.
But that is also a matter of perception and personal preferences. In the end, you can make it as complicated as you wish, being more sufficient than you need has no biological negative impact. It might have a mechanical impact, the more bottlenecks you put between the tank and pump the more power you need to turn it over.