Do I have to kill him to complete that quest, or can I slaughter Esbern?

Dude, there's a spoiler section for a reason, and this is pretty spoilerish. You've had an account for nine months, sort it out.

What dya mean sort it out? Should I climb a building n turn on the Mod signal or something to make em' move it?

SPOILER IN YOUR THREAD TITLE.

On behalf of all those who haven't progressed in what I assume is the main quest, thank you for your spoilerific tendencies.

WTF is wrong with some people.

Thx for the big spoiler, moron.

In answer to your question, I finished the main quest without even realizing you could kill Paarthurnax, or that anyone in the game wanted you to. So yes, there are absolutely other ways to finish the game.

Actually, I think there is a way around this. It might have been a glitch, but I was doing the bard's guild quest today and fast traveled to the dungeon (folgunther or rhannvig's fast or something?) South-west of there, and on my way I took a detour to check out the dragon symbol on my map (where you get one of the Disarm shouts). Before I got to the bottom of that hill, a normal dragon attacked me, and after I killed it, I strangely got the quest complete message and my log updated and said to return to Esbern. Note: the frost dragon guarding the shout was still there.

I was being an idiot though and after I got the shout I used become ethereal to jump off the mountain and it faded too soon, so I died and was back at Solitude before I fast traveled. Didn't get to go back to him.

I know that sounds sketchy but I'm not trolling. Level 40 now, main quest finished around 16. 360.

its a subforum called "spoilers" reading. its difficult these days.

Well this part of the forum is Called Skyrim cheats, Hints, and Spoilers. So you should expect to see spoilers with out tags here.