I agree with a lot of points he brings up, though I might be prejudiced since I belong to the group of people who are mostly annoyed at achievements. Though more at the way they're implemented (meaningless at best, grind-inducing and game-breaking at worst).
Now in general, I think trophies and achievements could be game-enhancing if done right, e.g. giving the player legit challenges or invite them to rethink the way they play a game. But in many cases, they are random "congrats, you're great maybe" popups on top of self-rewarding gameplay systems.
The way I understand the critique, it is arguing to give achievements meaning and make them part of the game experience instead of skinnerbox-style devices to have the player execute menial tasks. Compare Ninja Gaidens "kill 1000 enemies with weapon X" to Metal Gear Risings "kill bossencounter y without getting hit". Now one of them invites you to challenge yourself and get better at the game while the other just tells you "waste 5-10 hours with a shitty weapon you actually don't prefer". Same for "collect all item z in the gameworld", especially when they don't serve any additional value. And please remember how multiplayer trophies often tend to invite players to not play the game in the way intended or ignore tasks, which often takes away the fun for players who actually want to play a real round of MP (especially in team-based games, and even more infuriating if the trophyhunter then just disconnects after achieving their goal).
So IMO achievement systems need an overhaul. Not a "take it away!" but a way that allows to make them part of the game design instead of checkboxes and a way to allow devs who don't see value in them for their specific project to not being forced to include them. I know people argue that it let's them see their personal progress, though I ask myself - what about books, cds, movies, media in general. Do people really need a proof at hand that they finished a game? But to each their own, still please allow critical thinking on how to improve the concepts.