Domitius:
You are aware there are social repercussions for being a coward? Shunned at social occasions, your businesses stop getting customers and that sort of thing.
Dom has a bow and evasion so levitating fireballs inside the salon not so much as a challenge as you think.
So I am more than happy to deal with this in game, but since we're here, here are my thoughts:
1) I supposed it depends on who is going to consider Marik a coward for ignoring Domitius' challenge. From what I'm seeing in the OOC chat, the answer is not many. Domitius has spend way too long in noble court's to think people are going to care that much. Moreover, a quick check of the "Influence in Midmarch" page shows that Marik has a 21 influence in Midmarch and Domitius has a 12. I'm no expert, but that seems like a pretty big difference to me. Finally, I think it's probably a pretty good assumption that Marik's diplomacy skill is much higher than Domitius', so it's probably not a good idea to challenge him in the court of public opinion.
2) I was going to bring up what Andalon stated. It doesn't seem very honorable for someone who has likely trained with a sword since they were a wee child to challenge someone to a duel of blades who has literally never picked one up. Super courageous on Domitius' part.
3) Marik really doesn't care about Domitius' opinion of him. As he stated in the same rant you quoted above, Marik's mother was a whore, he doesn't know who his father is, and he grew up on the street. Honor doesn't mean much to him and he doesn't really care if Domitius (and likely very few others) are going to call him a coward. And again, given his influence in Midmarch I seriously doubt he'll be "shunned at social occasions", and Marik doesn't really have any businesses. Rather, he is one of the more prominent landholders in Midmarch and has a literal monopoly on all iron, gold, and silver mined in Midmarch. I doubt people will refuse to deal with him. Besides, with Marik's social skills, it won't take long for him to turn things around and make Domitius look like a bully.
4) If there was a duel with Marik using magic, Domitius wouldn't be allowed to use his bow. See, the equivalent of Domitius' challenge to a sword duel would be Marik challenging Domitius to a duel of spells...something I'm guessing Domitius wouldn't be very good at.
5) And like Marik (and now Adoven) have said, Marik simply stated the truth. Domitius swore an oath and then said he would not fulfill that oath. Does that mean Marik questioned his honor? I suppose so, but then it's simply the truth. The fact that "Henry told him too" doesn't change the fact that he swore the oath. That's just passing the buck.