I believe the author has hit a note here; Games need no longer be about "reaching" some predefined goal, they can be merely about exploring the space of possible actions or states contained within a rule set.
The Sims is a prime example here; Hardly anyone would contend that it isn't a game, yet it has no definitive goal, only an "arena" wherein actions can unfold. this arena consists of unbreakable rules; If you don't drink you die. Go too long without seeing someone and you'll get lonely, etc. etc. - All conditional statements. What the player then does is interact with the world - poke a little there, twist a knob here, and essentially just see what happens.
Only here does the goal-oriented aspect come in. The player says, e.g. "I want to stay alive for 24h," and then does what the player thinks is appropriate to make that happen.
Let's expand a little here; The Sims is too narrow to define a game from. Essentially all games do not carry a sticker that says "go here to win" - It is something the players decide. Take any shooter as an example; Some may claim there is a single way to win, getting to the top of the scoreboard, but in reality, this is a player-imposed condition. It's the player that says "I want to make that or this number higher than anyone else's." Sure, it might be suggested several places that this is the "goal" of the game, but in the end, it's up to the player.
I believe this is what the author means by "breaking the rules" - Playing in a different-than-intended way. Getting something "more," in some sense, out of the game, than what was advertised, and it is this resource that developers have started tapping into with achievements. Making an alternative playing style a goal in itself, and putting these to the forefront of the player's mind, means we'll explore a massively larger part of the game space than otherwise.
However, I also think there's a real downside to making the meta-game (Or rather, parts of it) stand out so clearly: It makes discovery a chore. Instead of some few thinking "Gee, wonder if I can get through the zombie apocalypse with only a pistol," you've got it staring them right in the face that it's possible and they should do it if they want the shiny icon, essentially downplaying a creative nerve, or, in the worst case, killing it completely by giving players a mountain to do and no room to explore.
TL;DR: Article good. Achievements killed the cat.