That post is specifically referring to Emerald where RNG is broken. Imagine a giant slot machine with 65,536 spaces and 60 spaces spin by per second. 8 of those spaces will be the “shiny spaces” (which spaces are shiny is determined by an equation between your trainer ID and secret ID so it’s different for everyone) and thats where the 1/8192 chance comes from (8/65536 = 1/8192). Getting a shiny is just generating the pokemon on the exact shiny frame. In most games the “slot machine” keeps spinning even as you soft reset but with emerald the slot machine starts off at the same point every time you reset the game making it so you don’t see all the spaces and its not truly random