I like to think of TTRPGs as "beautiful machines." This is to say that they are works of art onto themselves, and there is a value in their aesthetic qualities purely as aesthetic qualities. This much I think is fairly self-evident to those working in TTRPG design and those likely to stumble across this cohost post (copost). That said, I'm willing to expand if necessary.
Perhaps more controversial is the nature of TTRPGs as machines. They have an utility function, they turn inputs into outputs, and it is important that they work in achieving their function. This post from Ru's Roleplaying Rants is a great look at the nature of TTRPG as machine. Each game has its own function, which I may have been misrepresenting in the past as the idea of designer intention. Thinking in terms of function, I believe, will yield better results for designers.
The most common function of TTRPGs, I'd say, is providing tools for the players to create their own art. They may have additional functions, but let's narrow down on this one here. In providing tools to help create art, TTRPGs can be seen as paint or brushes or canvases. While a layperson might not see the impact of different brushes or canvases on a work of art (can't a painter paint whatever they desire regardless of their tools?) my understanding is that different tools can lead to very different outcomes. The sheer materiality of them impacts the creation.
I would go so far as to say that the content of games (as opposed to its formal elements) provide templates to things that could be created. D&D presents a different variety of potential creations compared to Apocalypse World. The formal elements of the game then, theoretically, should provide guidance to creating the things that the content points towards. They shouldn't show how to draw a circle and then ask the players to draw the rest of the owl.
That said, an experienced artist can use the tools to do things that outside of their expected function. A painter can use watercolors like oil, to yield interestin and unexpected results, though it will likely require a lot of labor and experimentation on their part. Following the expected function of a TTRPG, in contrast, should yield the expected results consistently and relatively easily. The player has paid for it, after all, and deserves their money's worth.
