So many people that 'get stuff done' in the 'work' sense are those who have good focus, set priorities, and focus on outcomes. They often don't even stand out.
Moreover, the 'I am special' is still arrogant, in a way.
Many of these people can have softer, beta type personalities, but the actions, decisions and and outcomes are still those of an arrogant person.
I know loud, boorish and apparently 'arrogant' people who are at the end of the day pushovers in the sense that they are actually nice guys, soft on negotiation because they want a 'fair deal', loyal to people to a fault etc., they just have a brusque, apparently cynical outward demeanor.
I think this is a very interesting psychological framework with the wrong wording in the title ... or rather, a much better definition of what they mean by 'get stuff done'.