Not sure about the Ability part of the question(will look for an Answer), but Moves do still get Beneficial effects even though there are Different Types of Weather. As stated in the Link you posted:
" Both Thunder and Blizzard have 100% accuracy, due to simultaneous rain and hail, while SolarBeam requires no charging due to the sun, but its damage is also decreased by 50% due to the other three weather conditions."
Abilities also get Beneficial Effects during this glitch as well. According to your Link, Abilities activate when this occurs as stated:
" If a Castform or Cherrim is brought into battle, their ability will cause them to constantly transform, thus locking up the battle until the game is turned off. Castform willonlytransform between its Sun and Rain forms due to those particular weather conditions being the first two to occur (and thus, Castform recognizes these as being the only two weather conditions on the field)"