I finished the previous post by talking about arrows skewering boxes.
You can also think about it this way: The boxes are full of legos. One box has boards, one box has the basic rectangular bits, one has minifigs and more technical bits and so on. Then you have an intention "I want to build a car" and you go through the boxes and find the right bits. That's the arrow, that intention. Lego cars come in various sizes, shapes and colours. They can be futuristic or retro, more abstract or technical models, doesn't matter, we want to talk about intention.
Everyone loves legos! "Let's play with legos!" is an invitation that's very much like "Let's roleplay!". Ok, so maybe I want to build a country house and you want to build a pirate ship (and someone else wants to do car crashes and a third is acting out a day in the life of Mr. and Mrs. Minifig). But then we're building/playing each on our own, we're all having fun, but individually. With roleplaying, where you have people sitting around a table in a social context that's probably not gonna fly as easily.
To understand the arrow stuff, you must accept that it's constructed around the premise that roleplaying is a social, collaborative activity, where we do something together, specifically. So when someone says "Let's play with lego!" the others say "Ok, what are we building?". It assumes that there is a shared intent. If you don't buy into that, cool, forget the arrows, read just the first post, stop here.
When we say "let's roleplay" that's not enough info. What's the intention? "Having fun." Yeah, sure, but we can have fun in many different ways (go to the movies, play a boardgame, drink and chat...). Why roleplaying specifically, what are we doing with it? What's our intention? Roleplaying is like boxes of plastic bricks. "Let's play D&D" is (in most instances) already a lot more specific. D&D is like a lego set - you know what's in there, what you can build with it, it's pre-picked stuff.
The first box is the group of real live people, remember? And the final box is what we're actually doing at the table. Game design, game texts: that's a way to pre-arrange sets of any number of elements (setting, colour, procedures, rules, dice mechanics, etc etc). It's a bridge between people saying "let's roleplay" and actually doing it (rolling dice, speaking). That's why consciously considering intent, the arrows, is important to game design, but not necessarily to an individual.
All of the above in one paragraph: roleplaying as an activity is a bunch of boxes with lots of plastic bricks in it. Game design/game texts are about inventing and arranging sets of specific bricks that allow you to build certain stuff (there's a "pirate ship" set, a "city" set etc.). You need to buy these sets or borrow them from other people or even invent them yourself to fill your personal boxes. Lots of people are cool with just playing with one or two specific sets. Some people want to rummage and tinker and make new stuff. Some sets come with the intention behind them, others are just assortments of stuff.
So you can start with an intention and get a set that was made to fit, or start with an intention and then rummage the boxes to assemble that fits, or get a set that has an intention and adapt yourself to it, or adapt and existing set to your needs, or just rummage and get inspired with intention from random assortments. Bottom line is, you've got an intention, some orientation or goal as you go from "let's play" to actually choosing and assembling bricks in specific shapes/talking and rolling dice.
The final post is about the categories the model assumes.