I think the latter is probably more pleasing for most personality types. You can still come off as the "nice guy" in polite company, even though you're being very demanding. Think how much warmer people like Sundar Pichai come off as compared to someone like Larry Ellison.
I also think there's a salesmanship aspect here. Its easier recruiting if you sell your company culture as a "nice" place led by a "nice" leadership. I think its a harder see to say "Look we're assholes here but the job and pay is good."
A wise leader surrounds themself with people they can truly trust in. In this message we see a glimpse into the dynamic between Bill Gates and Nathan Myhrvold, and my main takeaway is that Bill truly trusts Nathan here, enough to be vulnerable and speak openly about his worries.
While it's humorous and perhaps even enlightening to think of him as a "child king", I don't think he was only "seeming hurt" here or manipulating (unless you count all forms of emotional appeal as manipulation). Being honest and straight is a very effective way to lead those close to you.
It's also the leader's job to worry about threats like this and direct the attention of his advisors.
That's what I was trying to point out in my original comment. The "nice" and "hurt" leader is a common ploy and it gets results.
Even if Bill Gates has the dark triad traits I do not think they were on display in this particular email exchange. I truly don't think they were engaging in any "face-saving" here -- Nathan had been working for Microsoft for 10 years at this point, leading Microsoft Research and rising to the first ever Microsoft CTO. They coauthored a book called "The Road Ahead" in 1995. Bill has called him the greatest hire he made at Microsoft.
From every single source I've come across it seems clear that Bill Gates and Nathan Myhrvold are friends and share a deep mutual respect. No wonder they are still working together in 2021! You'd think after a lifetime of supposed abuse Nathan would have stopped working with him after becoming a billionaire, right?