The wiki said that this random challenger is a radiant quest. It says the quest giver is the challenger.

I do not get any kind of quest in my journal from this.

He just challenges me at random.

Is this supposed to have a journal entry associated?

It's supposed to pop up under the misc. quest section of your journal after he's issued you the challenge. It's something along the lines of defeat the dueling wizard.

I had to look this up. In my 100's of hours of gameplay (including my current Mage with 100 hours and 100 skill in every Magic school), I have never once encountered this quest. Weird.

This is what concerns me. He challenges me. I have 2 dialogue options: 1. "You'll have to find another way to stroke your ego (decline)" and 2. "It's your funeral."

Either option still results in him attacking.

After the battle commences, I do not get anything that says "defeat the dueling wizard" or anything of the like.

Probably completely coincidental but I never see him until after I read "The Apprentice's Assistant" which details how to do a 'proper' mage duel.

In this book, does it mention using a Dragon Priest staff as a violation of the rules?

I don't want to break the rules in this battle, but the spells I currently have are not hurting him.

I have my game saved just before he approaches me.

Heck, I used my sword to kill him.