Dynamicland and Dynamic Reality Overview
As someone who is interested in the intersection of STEM and the arts, I'm a big fan of Nicky Case's blog, and in their most recent post (as of writing) they reference Dynamicland (I would also recommend checking out their youtube).
Tl;dr it's an approach of humanistic computing, taking compute off of a screen and out into the world.
They do this through a tech stack that seemingly involves lighting and cameras, and mapping physical objects to code, it's not open source but that's how I understand it, but anyway it's less about the tech and more about the approach.
The creators seem like brilliant people and they make some profound insights about computation and this notion of dynamic reality (as compared to virtual reality, augmented reality, or of course physical reality).
So Dynamicland inspired this post, but this is about TTRPGs now. If you want to learn more about Dynamicland I'd encourage you to watch their youtube videos.
The TTRPG Stuff
Presumably this is what you came here for. Basically, what are some presumptions about game design that use mathematical or linguistic abstraction, that might be better represented visually or kinesthetically?
Character and Inventory Management
You ever lose track of your abilities and items? Not anymore you don't.
Meet Orcus Johnson. He has a laser axe (A1), shoulder mounted blaster (B2), and the Johnson Crown (C3). More details can be found mapped to those keys.
It would probably be both easier and more in the spirit of DR to use a hand drawn figure, or like some combination of a drawing, paper cutouts, tokens, minis, etc., but I'm still a very digitally oriented person. Also, if you can draw, you can do something besides a stick figure.
It would be especially fun to do this for Mecha.
Wounds
We were talking about this on my discord server so that's part of what came to mind. The idea of having targeted attacks, like being able to wound arms, legs, etc., with various status effects like burning, bleeding, acid, always sounds like fun, but it can be a huge pain to keep track of. Until now.
We can see clearly that Orcus Johnson has lost his leg and is bleeding profusely. Additionally, Thor Goldberg struck him with lightning and he is now electrocuted and stunned.
The point here is not to get rid of the mechanics or math or whatever, this figure corresponds to bleed effects, lightning effects, etc.; it's not less crunchy, it's just more immediately identifiable what is happening. Rather than a bunch of abstract numbers or words and having to dig through it all, you can see very clearly what's going on, and then trace it back to its references.
I'm not really into crunchy games anyway, but if I were to try to reincorporate some crunch into my gaming, I'd probably try things like this.