The focus of the article is primarily around how to simplify existing games and gradually build them back up. Unfortunately many games, like you say, have a very large number of parts, but it's not straightforward to modify gameplay to not require them while still having an interesting and balanced game.
I really wish more board-games had a "low-parts mode" or a "trial" mode where you could experience the gestalt of the game without having to cram all the minutiae. Basically: do what this guy did for his daughter but put it in the rule book.
I collaborated with the designer of the notoriously complex, 23 pound box game Gloomhaven to do exactly this for the upcoming small-box, mass-market oriented Jaws of the Lion. We built a 5 scenario on-ramp tutorial I called Fischer-Price mode.
We included new, simpler, components in the game that are exclusively for this tutorial, have players add mechanics and components and systems one or two at a time. During playtesting we went from about 2+ hours to read and semi-understand the rules enough to play, to playing in about 10-15 minutes.
It can be done, but it can add significant cost (materials, development time) to the game.
I don't get any royalties, but you should! I got one of the early production copies and I'm two scenarios from finishing the campaign with my wife. It's lots of fun.
Yup! If you're playing with two, I might avoid the Voidwarden. My favorite class, and it's playable with 2 players, but definitely harder with only one ally. All other combinations work very well together at 2 player though
For example we got Carcassonne recently and it includes an "extension" (Abbots & Farmers). The rules has an additional sheet, so you can play the raw game and pick up the extension later once you've grokked the normal rules.
Settlers of Catan does a similar thing, they have a slightly more basic gameplay in the rules for people starting out.
And 'without farmers' is precisely how I introduce Carcassonne to new people. You have to be pretty good at spatial reasoning to understand farmers and their fields in the game just from someone describing it to you. But most people get it right away (after the first game) when I say, "we'll play one game without farmers, and then look at the finished board so you can see where the fields and their borders are."
Of course, that only works for a game like Carcassonne which plays in 45min or less on the first go and can get down to 20min if you're playing with people who know the (base) game well.
In some ways rule reveals/progression is a defining feature of the "Legacy" style of board games. Generally the focus on such games isn't about rule reveals/progression, because the core idea of Legacy as a style is about board games with permanent changes that last through a story campaign of some sort, but rule reveals/progressions/rule tweaks are key storytelling tools in that style.
Some of the games are notorious for having half-empty rule books that you will eventually fill with stickers for more rules.
One particular well regarded Legacy game for it's slow, careful reveal of rules is Seafall (which is noteworthy for being the first non-licensed Legacy game by the Legacy genre's "father" who built the original Risk Legacy and has contributed to many others like Pandemic Legacy). I've got it on my shelf and have been hoping to find the right group to play it with, so I've mostly tried to avoid spoilers, but the way it was described to me is that it is a full 4X (strategy gaming acronym from videogames for Explore, Expand, Exploit, and Exterminate) that starts with only the rules for Explore and expands out from there. (And it is proper exploration with players encouraged to sharpie their discoveries to the board.)
One game with a version of this mechanic is Fabled Fruit. It's a worker placement/ hand building game. There are 6-10 possible actions you can take each turn: the initial 6 are relatively simple but as the game goes on, old actions get discarded and new ones, often with more complex mechanics, take their place. You're encouraged to keep the game in the new more complex state the next time you play it.
Even the initial state is too complex for young children but it might suit what you're looking for if that's not actually a requirement - I don't think you'd really enjoy playing phase 1 of his Carcassonne adaptation either.
I really wish more board-games had a "low-parts mode" or a "trial" mode where you could experience the gestalt of the game without having to cram all the minutiae. Basically: do what this guy did for his daughter but put it in the rule book.