The swap glitch is what makes the current any% route possible. The ability swap had been known about for some time, but was only utilized in Land's End on the trampoline. Now, the glitch is activated when Mario jumps to hit an invincibility star, but opens the menu while jumping.
To open the menu, get under the star chest, then press B then X immediately after (a few frames to do this). Once in the menu, you switch the characters where you want to swap abilities. In this run, the first switch is Mallow's Shocker on Peach. Mallow learns Shocker at Level 10. Peach is Level 9 heading into the invincibility star, while Mallow is Level 6. When you switch Peach and Mallow in the menu, Peach will level up to Level 10, but be in Mallow's slot. Mallow will level up to Level 7, but be in Peach's slot. This is why Mallow appears to get Level 10 and Peach appears to get Level 7. They represent each other, since they switched. Since Peach hit level 10, but is in Mallow's position, she learns Mallow's Level 10 ability, Shocker.
The same is done with Geno/Peach at Peach Level 14.