This quest is still bugged.
I'm playing the latest version (V3.0.160.28) and I'm having the same problem. Arran does not give me the key after defeating Murga and Voidwoken in the arena.
The log book stops updating after "We defeated Murga - the Champion of the Arena - and a Voidwoken that joined the fight."
The log book is supposed to continue with, "One of us is now the Arena Champion of Driftwood," and
"Arran granted the new champion a key that will unlock some treasure. He remarked that there will be dangers near it however, adding that it truly takes a champion to claim the prize."
The quest just dies right at the end!
