yeah i don't think the video explained it well
i think it pretty much refers to people that want to dominate aspects of inter-player interactions. they're players that want power. i feel like it's hard to find good examples of games that pander to this, but agar.io might be a good example.
I think the best example would be your standard First Person Shooter online player.
The guys who strive to win every match of CoD or Battlefield or Halo.
I don't think they quite count as Achievers, even though they want to be good. They want to kill and be good at it. Dominating the enemy team, or enemy players is their goal.
But it doesn't necessarily make them nasty (although it does facilitate nastiness).
For me, I think I am an achiever, if not a slight explorer.
I like to play the games and I like to get achievements. I don't dedicate myself too much to getting those, only if I think they're in my grasp, but that's how I like to play.
Socialising is not really my thing in games, I much prefer to stick to myself or with friends I already know.
And Killing is something I'm not interested in. PvP has never been my passion, even when I do well at it.