It seems to be some sort of select glitch (pressing select as if swapping two items or Pokemon) and a pointer glitch.
Basically, the run appears to do this:
1) Get the Potion from the guy on Route 1/2, and get Oak's Parcel from the shop.
2) Go back to Pallet Town, then, in the item menu, attempt to switch Oak's Parcel with Cancel.
3) Get into a battle. In battle, attempt to switch Pokemon with itself (?) or some invisible glitch. Defeat other Pokemon. Pokemon levels and graphics glitch.
4) Walk around Rival's house 3 times (?). Enter door. Warp near Celadon.
5) Enter and exit the building to Saffron. Enter Celadon, enter and exit the Pokecenter. Enter and exit the building to the left, then go near the Mart.
6) After some wandering, enter the Mart.
7) Beat the game.
It seems the wandering has to do with step counts in some way.
From gocha's "dokokashira" hint, I found the relevant thread:
http://pokemonbug.oh.land.to/rgb/711worp.html
But I can't really read Japanese.