If you watch closely at the first "flex" mention (24:50) you'll see that Court is wrong about the cause. The swing arm itself isn't deflecting, it's the center pivot arm (not sure what that's called) which is pivoting on its bearings. This is the arm that translates the swing arm up/down motion on one end into the in/out motion for the rear shock at the other end.
Here's an arrow pointing to the center pivot arm:
View attachment 71467
Here's a shot from the video:
View attachment 71468
When watching the video on your computer, go full screen and place the mouse cursor at the rear arrow (leftmost in the above photo), which is where the swing arm joins to this center pivot arm thing. As Court uses throttle and the shift interlock re-enables you'll see that point move laterally (up/down on the screen relative to the cursor). The swing arm itself doesn't appear to deform as much as there is play somewhere in this multi-pivot mechanism. Note that the distance from the center pivot to the rear swing-arm pivot is pretty big so any small play in the center pivot gets magnified out by leverage.
Maybe this is something that can be adjusted or maybe it's something in the quality of the bearings used, or maybe it's just this particular example.
I also note that in both this section and the later section, where Court is climbing a short steep hill, he's in the top or almost top gear. In the second section of the video, he's again using only throttle and is going too slow and up too steep for that top gear. The top gear (small sprocket at the rear) isn't meant for hill climbing, it's meant for high speed on level or downhill ground.
I'm also not understanding the rear brake "zing" thing, either. The wheel, the brake disc, and the brake caliper are all attached to the swing arm. So, even if it deflects (or pivots as shown above), that shouldn't affect alignment.