It's a Khornate fleet because it's Tzeentch's fault.
Khorne and Tzeentch aren't actually dire rivals. Tzeentch hates Nurgle a lot more...
But it can easily be a Khornate fleet anyway. I think having it be Khornate adds a little more interest really.
Khornate fleets are often built around boarding actions. A relatively effective tactic in regular combat, particularly with powerful Khornate boarders. Ships are able to take enough firepower to close and board against most foes. The prizes from successful boarding actions are immense, with the potential to both please Khorne with wanton sacrifice *and* get a juicy new warship under your command. That would be woefully ineffective here. Let's assume that the Khorne admiral hasn't themed his fleet around boarding. The discussion on Khorne admiral behaviour under "Powers of Chaos" is that they are first and foremost effective commanders, but will close to board if they have a chance.
Where is the idea that Daemonships attack telepathically coming from? They don't do that in Battlefleet Gothic. They radiate a (fairly short range) aura of unease that makes it harder for enemy fleets to coordinate, but they don't do direct mind attacks.
Daemonships are basically regular warships in their method of attack. Where they step up is in defensive abilities. They can easily ghost in and out of the warp, and they repair (heal?) damage at an insane rate. It is very hard to slowly whittle down a Daemonship.
EDIT: I'd also say that there will be a *lot* of safe zones when fighting with tactical FTL. The enemy has no idea what angle of approach you will take. You can be any direction or side of them in a millisecond. The Chaos fleet does not have enough firepower to blanket a 360 degree sphere of space around them with weapon fire.