For what it's worth, I was absolutely aware of the Berlin interpretation and was giving it about as much attention as I think it deserves. In my opinion the Berlin interpretation is not a sane definition of a roguelike, it's a point-by-point description of what the common roguelike of the day was. It's a ridiculous gatekeepy way to design a genre; just imagine the definitions we would have got if "first-person shooter" had been defined in the wake of Doom ("a first-person shooter involves using a set of six to twelve weapons, bound to the number keys, to kill demons") or in the wake of Battlefield ("a first-person shooter involves large team battles with matchmaking and gradual unlocks of sidegrades, which can be bypassed by paying real money").
But the point of that post wasn't to attack the Berlin interpretation, rightfully or not, it was to trace the outlines of a concept that I think a lot of people aren't isolating. The existence of the Berlin interpretation - which was a lot more popular back then - was, and to some extent still is, blinding people to the interesting parts of the genre. The interesting part of an FPS is not the exact number of weapons available; the interesting part of a real-time strategy game is not the fact that units move smoothly, and not on a grid; the interesting part of a roguelike is not whether it's made with ASCII art. It's an implementation detail.
My attempt in that post, made kind of hamfistedly as anyone would say about something they wrote over a decade ago, was to get at the interesting parts of a roguelike and try to draw a loose outline around them.
If I were to write this today, I'd spend a lot of time talking about the XCOM 2 expansion pack, which I think made some fascinating steps towards being this kind of game. Yes, specifically the expansion pack.
In the base game, you can more-or-less plot out your build order before you start the game; you can know what will show up at every step, you can know when you'll get certain items, you can roughly predict when you'll get certain abilities (modulo soldiers dying, of course), there's no unpredictability.
In the expansion pack, though, they throw a bunch of random events at you that can seriously influence your build order. Maybe you get double-speed research, for a single research item, that you must either cash in immediately or abandon; this can mean you're encouraged to pick somewhat-random equipment. You can also be given the opportunity to buy weird unique items that are permanent upgrades to, again, somewhat-random equipment, so maybe in one game shotguns are really good and in another game it's sniper rifles that get the random bonus. Again, this can change your strategy significantly. And finally the big enemy monsters have random traits - they're weak to things, strong to other things, and all of this is re-rolled every game.
This isn't an enormous amount of variation. But it's significant, and this is the thing that I'm pointing at; situations where the player is left thinking "wait, hold on, how do I navigate this? how can I put these bonuses and penalties together into something really awesome for me?"