Physical attractiveness can play into it, but there are some very charismatic actors who aren't attractive. Acting skill plays into it, but often charismatic actors are only mediocre at "acting". It's commonly associated with confidence, but some charismatic actors have a habit of playing un-confident roles. (Which is not the same as a lack of personal confidence, but what is it they're doing that conveys both "confident" and "insecure" simultaneously?")
It's often said to be about commitment, a sense that they're really "present" and really focused on you. That's certainly something we want actors to do: the more they care about their scene-partners, the more the audience will be drawn to both. (That's true even when the focus is based on a negative emotion, like hatred, but it has to be a really targeted kind of hate and not just a general anger.)
I can teach a lot about the theory of acting, but I have only a vague idea of why it works. When it does, it can be really potent, though it can be be incredibly hard to get. People will often do the same wrong thing harder. A lot of the silly acting games they teach are about getting you to at least do a different thing than what you were doing, hoping that somehow you'll accidentally discover the right track.
I'm not sure any of this is really "charisma" in the sense that this writer means it. I certainly support his overall gist: soft skills are massively underrated.