Having given this a little more thought, I'd say these are the key things the DXV games have to give them their unique feel. Note I wouldn't say you necessarily need ALL of them, and occasionally some might get broken (think Black Market) but in general I think these are the things that matter.
Modular components: You only use some proper subset of the components each game
Large impact: The modular components selected are one of the most major impacts on the game. Games will play very differently depending on what components are selected. As an example, Terra Mystica has bonus tiles and scoring tiles, and they have a reasonably big impact on races and strategies. But their impact only really makes some strategies a little better or worse, it's rare for it to make specific strategies become suddenly much more powerful, and the like.
Visibility: I think this is key. While many other games might only see a small subset of components each game just by virtue of a deck being too big, or nobody activating certain mechanics or the like, the DXV games explicitly show you what's available and by deduction, what isn't. For example pops mentions Innovation - and while it's likely a lot of cards won't be drawn (heck, ~10% of the cards in base aren't available due to achievements), you don't know in advance - you can't plan for the fact that Gunpowder isn't in the game because it might be, every time.
Huge variety: A little hard to quantify, but the amount of possible options should be massive, typically in the millions or billions of possible options, just in the setup. For example, Tzolkin has its monuments, but you only ever select up to 6 from 13 - which is only about 1,700 different options.