Square isn't public so I imagine that the private stakeholders either are OK with him taking the job or aren't able to stop him (if he owns enough stock).
The role of a CEO and an engineer are typically much different. Most would probably say that being the CEO of two companies isn't feasible. However, some of the most important parts of a good CEO are hard to replace. A part-time CEO with strong vision and leadership may be able to more effectively lead a company towards success than a full-time one without the right vision or leadership.
By having trusted and capable senior leadership in each company, so that the CEO job is limited to managing that team and harmonizing disagreements among them.
But it's important to remember that Elon and Jobs were unicorns. It should be an immediate redflag if people compare others to them. I also think it's unfair to compare Square/Twitter with SpaceX/Tesla or with Apple/Pixar.
Also the above commenter's point, talking to people 16 hours a day does not mean you're working. An engineer's work is quantifiable, so they can be held accountable when they claim they work 16 hours a day. Not so for a manager. Their effect (good or bad) is far more difficult to quantify.
I doubt it works like this, and if it does, it's exactly why people think it's a crazy idea. Do you really think it's possible to be the CEO of a major public company, one that's changing the game and has a very high profile, and have a schedule where you take three days "off", to work elsewhere?
I read that Dorsey basically divides his day into Twitter in the morning and Square in the evening, or something to that effect. I believe he lives walking distance to both offices in the Mission.
For accuracy's sake, he must live in the Tenderloin then, maybe at the NEMA apts. Twitter and Square are both in the Tenderloin, the Mission isn't really walking distance to that area (right on Market).
edit: Alternatively, he could live in the mission and then walk between the 2 offices during the day, they're right next to each other.