Nidoking is not an Isle of Armor Pokemon.
Nidoking, along with many others, will be legal on Pokemon Showdown! once Crown Tundra releases sometime in the Fall (likely November).
You can
search it up and find the list of Pokemon that are set to return by then.
Also, make sure not to mix it up with Random Battles because the manager of the format decided to add all Pokemon that have been revealed to return prior to Crown Tundra. That said, most of them are not legal yet, but they are available in Gen 8 randomized formats.