I worked with a bunch fo ENTJs (and also IXTPs and IXTJs) in a corporate environment and y'all terrifying. And that works because in certain environments you are greatly rewarded for how competent and terrifying you are in as much how much you can cow the other sharks into submission.
And when success is based on meeting parameters or quotas etc. and people are expected to be cutthroat and/or tough, you aren't expected to care if people like you. As long as they respect you. And they will if and only if you get the job done.
ENTJs politic in their own way, they are very calculating and they base it on external factors, like the targets your are supposed to hit on paper. You may notbe affected personally or emotionally if people like you, but you know you have to get votes so you'll do what needs to get done. ENTJ's also know who are the power players the people you must impress, what is considered prestigious and 'correct', the people you can dismiss because they have no clout. I actually think ENTJ can be very hierarchal and even tyrannical in this way. And traditionally traditional leaders follow a hierarchal power structure and approach.
The fact that the NT makes you care less about people's feelings or how they feel about you personally is actually a great boon in certain environments like the corporate world and I'm going to go out on a limb and say the military.
And there is a lot of politicking that goes on in both realms though it may seem much more straight forward.
It helps a lot in politics as well because it gives you the very tough skin and calculating mind you need to win and stay in office.
I also can't help but read a bit of...pride in the description that ENTJs can't play the political game well? As if there are types that are 'above' politics? Politics gets a dirty name but it's an integral part of life and makes the world go round.