"The Xbox 360 has their achievement system too"? I think they were the first out of all the examples you list.
One of the first major introductions of mainstream achievements happened with the Xbox 360.
I did mention that the Xbox 360 was one of the first mainstream applications of gaming achievements. I didn't give my original list any chronological preference
Achievements are little more than a public way to show how far you got in a game.
That depends on the game. Many times achievements reward different play styles. Did you use a single weapon the whole game through, or did you choose variety? Did you beat it on the hardest difficulty? Did you go find every last hidden treasure? Did you do the optional content? They might not be the most exciting thing, but perfectionists and friends (as well as show-offs) often enjoy the ability to back up their claims of truly completing a game.
Arithmetic is being able to count up to twenty without taking off your shoes. -- Mickey Mouse