IMO the Red King is (was?) absolutely an Outsider ally, but is not one of the 13 "nemfectors", same as Lord Raith.
Red Court vamps are with 99.9% certainty a similar "hybrid" and/or parasite state of "lesser" outsiders with mortals, like the White Court are, especially given the fact they've had much more blatant/obvious Outsider theming and influence throughout the series.
There's also one crucial fact to consider... do these 13 nemfectors have to permanently inhabit a single someone/something in the material world, or can they infect multiple beings, but can only actively control/observe through one of them at a time each?
I don't think this was ever actually clearly stated or clarified/mentioned in the stories nor WoJ.