I'm playing on normal. I've tried just "strong jumps" while holding the jump key all the way, they stop before reaching the 3rd-last sparkly thing. If I try a weird not-quite-full-height jump, go from the very edge, it sometimes seems to catch a particular spot of acceleration and reaches the 3rd-last or 2nd-last sparkly thing. I must have tried it over 200 times with all sorts of variations and have never gotten closer.
Edit: looking at that jump and at the others in that video (such as over the spikes, immediately following it), it appears that maybe the air zoom things don't give Keen the same speed in my version as in his. If I just jump into it from the right side as he does, rather than run to the very edge of the platform and jump up into the bottom, it doesn't seem to get me anywhere near the other side...
I'm really tempted to just use a flying cheat code for this jump, if that exists here.