This isn't correct information anymore, in my opinion. Chess engines have improved tenfold over the last four years (when the author says he stopped playing). The increase in the strength of chess engines has subsequently caused an increase in the "humanity" of chess engines, meaning that, instead of playing bizarre moves that are strong yet incomprehensible to humans, they play principled, sound moves that are strong tactically and strategically.
The main thing that you will miss as a sub-2000 player (or ever, really) is tactics, which is exactly where computers excel. A computer will be able to tell you tactics you missed and will allow you to experiment to see how different moves would have improved your game.
I agree that you should analyze games with your opponent after the game (and also with stronger players), but keep in mind that, if you're both sub-2000, you'll both miss obvious tactics even as you review the game, which doesn't really improve your chess thought.
One last thing: the 400 points in 400 days training comes from the book Rapid Chess Improvement, which I do not recommend for the beginning player (the knight exercise is good, though). In it, Michael De La Maza wastes time blasting Jeremy Silman and the strategic approach to chess games. Some people like the book for the mild drama it started, but the tl;dr is "tactics, tactics, tactics," which pretty much everyone will tell you.