While deadly arena fights do definitely sound more chaos than loyalist, I'm kinda surprised they aren't a thing for marines. I get the impression that you kinda need to have a constant stream of casualties to produce geneseed, and honorable combat seems like a good way to do that safely.
Couple things:
1. Space Marines do have feels you know. They form bonds of friendship and brotherhood (brotherhood being essential to their mission.) Their mandate is to die fighting against the enemies of the Emperor, if they must. Not to die fighting each other. So while it's easy to assume they're automatons, they do have feelings and opinions and killing their own would lead to a pretty poisonous environment, unless their chapter outlook is seriously warped.
2. Each Marine can represent
hundreds of years of battle experience and wisdom. A newly minted Space Marine, while by no means harmless and having dozens and dozens of years of training and combat experience, is still less than a veteran. Space Marines only get more dangerous with age.
3. Training new Space Marines, like I said above, is a pretty time intensive investment. Only a crazy chapter would jeopardize their strength for a pastime like that. I can see it under pretty rigorously controlled, and ritualistic, circumstances though.
4. Space Marines are usually pretty practical, and analytical, maybe even to a fault. You have to go renegade or Chaos, and get away from the constant DO YOUR DUTY mantras of the Space Marines to lose that mindset. As I said, to waste a veteran marine in bloodsport is very impractical.
5. The Inquisition tends to look out for signs of this kind of lack of discipline as an indication of slipping toward Chaos. For example, this kind of Deathmatch is entirely in keeping with the Worldeaters, what with Angron's back story of being from a gladiator world, them worshipping Khorne, and being homicidally violent with everyone, including each other. Spilling blood for Khorne is honestly their highest objective. Compare and contrast that to a loyalist chapter, whose highest objective is killing the enemies of the Emperor. Get the drift? The Codex Astartes models what the Imperium generally considers the ideal space marine, and is the rough measuring stick for what the Inquisition might use to judge a Chapter's deviance. I'm pretty sure an assumed tenet of the Codex Astartes is "Don't murder your fellow battle brothers, it makes it hard to fight a war." Then again, there's lots of stuff Chapters do that isn't mentioned or covered by the CA.