Looks to me like he's using the high-angle passes to force the burr to turn to the back side (the flat contact face), after which he flips the pruner around and (presumably) scrubs the burr off.
I have a similar sharpening tool from Fiskars that I've used for sharpening my bypass hand pruner (also Fiskars). It's diamond on on side, and simple chromed steel on the back. They suggest using the chromed back side of the sharpener to de-burr from the flat, inside contact face of the pruner's cutting edge, much in a similar manner to that shown in the video. I DON'T use any high-angle passes with the edge of the sharpener, as shown in that video - I've found that just sharpening in the initial manner shown is enough to get a burr turned toward the back face. Just test the edge with a fingertip to feel for that burr - the steel is pretty soft in such tools, and it doesn't take much work or time to generate a burr that's easy to detect.
The cutting edges on these tools don't need much detail work or high refinement as we might be used to doing with our EDC knives. Just apex the edge with such a tool, or a file, or any other sharpening device that can 'fit' sufficiently between the pruner's jaws and sharpen in the sweeping manner shown. Sometimes it's difficult or tedious to sharpen the cutting edge in a purely perpendicular manner, as we'd usually do with knives, as the other side of the pruner's jaw gets in the way. An alternative is to disassemble the pruner to give better access to the edge. I've done that also - but I've found it's usually more fiddling than is necessary for these tools. So I don't disassemble to sharpen them in such a manner anymore, unless I might be doing so for another reason, like extensive cleaning, etc.
I'd personally never use an abrasive tool on the flat backside of these pruners (incorrectly referenced 'sharpeners' earlier; corrected by edit). Anything taking metal off that contact side is begging for cutting troubles after the fact, if the contact faces can no longer meet crisply. No amount of tightening of the pivot will fix that.