I don't recall having to kill him, story wise. I blasted through the main story line using the console (And before anyone says anything, my first character was intended for legit play, but he got bugged out, and I couldn't find any console commands to fix it, so I said screw it, and made a new character, super powered her, so I can see the ending of the game.) Anyway, IIRC, after you kill Aulduin, and you're taken back to the throat of the world, there's quite a few dragons flying around, then Parthanex talks to you, and then flies off. I haven't went back to see if he's still there, but I'm pretty sure you can play through the whole game without killing him, unless there's quests to restore the blades or something, and you're wanting to do that. With that game, I didn't kill him, nor will I. But with my next character, I think I will. On another note, I don't have a problem with Delphine, and didn't even know she invited herself, until I read the posts above. The person who I didn't want there, who I decided to let stay, was the Thalmor woman, which I'm surprised she didn't do anything to me after I murdered her men.