I modified my original post to try to make it more clear what it is I'm asking.
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Ah, I see. I did not notice the pattern in your question. You covered most of the interactions I can think of. Besides those I can only think of new levels of interaction with those at the surface. What I mean: territorial wars might be hard to identify on the surface because it consists of separate battles at different times. If the player manages to catch a glimpse of something deeper going on it might be super interesting. I would totally set up camp where I think might be the next battle location. I guess for this to come up either you code these scenarios specifically or you have a very sophisticated AI.
I think for your example, there could also be ways to make territory locations visually obvious to the player if they can't just force such a conflict themselves(e.g in rainworld you can just lure lizards and watch them fight, while JPOG you can just create dinosaurs next to each other and they'll usually fight immediately).
While I don't know if it's has ai territorial fighting yet, Wolfquest 3 has systems to show players where wolf pack territories are located.
I find the games I play that have these systems... I never even know they are there until I hear about it in a dev interview or something. The player isn't going to notice something unless it happens right in front of their face and to do that you can just script some cool/unique interactions instead of building a dynamic system to support it.
"cool/unique interactions instead of building a dynamic system" feels a bit vague. What do you mean, and why did the examples I give not count?
With perhaps the exception of skittishness, most the examples I mentioned are very visually obvious (such as a wolf grabbing onto an elks leg to keep it from running, a lizard snatching an animals with it's tongue, a rex chasing a raptor that itself moments ago was chasing an even smaller raptor).
That said I do know what you mean about the value of something being visually obvious or interesting to look at rather than being complicated. One of the points of this thread was to see what people find visually interesting.
Unless your game is designed around it (something like Monster Hunter comes to mind) I think you need to keep it as simple as possible. I think players will always prefer a memorable (if simple) trait over something realistic that they either don't see or don't understand. Even something as basic as "these monsters can attack other monsters" is enough
Take Breath of the Wild. It's been years and Twitter is still full of gifs of a Guardian vs. a Talos or a group of moblins fighting a bear. There's very little 'special' about these interactions - it's just their normal attacks with their default behavior - but we love to watch it because it's often something we stumble upon by accident
Rain World goes the complete opposite direction where the majority of the game is figuring out how to read creature interactions with each other and their environment. I don't really dig that game, but what I think makes people attracted to it is that creature interaction becomes something like a puzzle. There's really no 'wasted' interaction (meaning everything they do is relevant to the player) so studying them and experimenting with them is a lot of fun
Then there's No Man's Sky which has just dreadful interaction. Everything feels random and nonsensical. Did that creature run away because he's skittish or was it a random thing or was it a glitch? I don't know, and I don't care, because it's not relevant to me unless I want to scan or take a funny picture.
I don't really play monster hunter, so could you clarify what you mean? I thought it was just a typical, slash-it-till-it-dies game where ai interactions weren't really all that important to the game?
As for things be relevant to the player, what's relevant to varies between players. For your average gamer, watching creatures do their own thing isn't relevant to them at all and what you've said is totally correct.
But for people who are really into animal stuff, like the sort of people I've seen who play animal-based roleplaying and sim games, or zoo games (e.g WolfQuest, Saurian, Shelter, Tyto, Zoo Tycoon, Jurassic Park Operation Genesis) watching animals live out their lives is relevant to them. For JPOG in particular, all the time I hear people bring up how they prefer just watching the dinosaurs over the actual zoo-building and management aspects.
For Rainworld, while there are probably plenty of people who like interactions only because it's puzzle-like as you said, I know plenty of people just enjoy how lively the creatures feel and enjoy watching them do their thing.
Of course those people are probably more of a niche group that's only worth looking into if you're actually making the sort of game that has them for a target audience.