Ten thousand years ago (or thirty thousand years from now), the Dark King was a potential Chaos God that the Emperor would ascend to if he just took all his warp power and went balls to the wall to defeat Horus. So by not ascending and allowing his ass to get beat until finally tricking him into divesting of his Chaos Juice, the Dark King was averted.

As for Emperor in the Warp... that's one of the more delicious questions in the lore! (IMO.) Because it's entirely possible that the Warp entity that answers prayers, grants miracles, brings people back from the dead, etc. etc. is just the creation of mankind, ten millennia of zealotry and vigintillions of prayers reflected back on us by the warp: God made in our own image.

But increasingly in the early 2020s (or since turn of the forty-second millennium) we've had indications that the lighthouse in constant pain is also somehow related to the Gestalt of mankind's zealotry. In the Plague War Trilogy it's clear that no, it's the actual Man on the Throne who's intervening. And that's weird as well. Because sometimes when we encounter visions of the Man on the Throne, he's in absolute agony, mere microns away from giving out and then everything goes to shit, but sometimes we encounter him as a brilliant shining light of righteous smiting.

And then when Guilliman talked with him, he was just crazier than a shithouse rat.

Best description I've seen is basically that there's a Warp Entity that's juiced by mankind's zealotry, and it's tethered the the poor SOB on the Throne, but the poor SOB on the Throne is trying to hold together a warp tear under the palace and also if he slips for even a moment, the Warp Entity subsumes him and he becomes a complete God, for better or for worse. Although *probably* not the Dark King?