“Well, he is very talented,” Mr. Trump said. “Anybody that takes over a situation like he did at 26 years of age and is able to run it, and run it tough. I don’t say it was nice.”

It’s not that Mr. Trump doesn’t grasp the depths of Mr. Kim’s butchery — he just thinks such cruelty shouldn’t get in the way of a good deal. As he said in his postgame news conference, the waterfront real estate possibilities are awesome: “They have great beaches. You see that whenever they’re exploding their cannons into the ocean, right? I said, ‘Boy, look at that view.’ And I explained, I said instead of doing that, you could have the best hotels in the world right there.”

Dealing with men like Mr. Kim is, on some level, comfortable ground for Mr. Trump. Such negotiations are a higher-stakes, global version of the world he came up in, one of cutthroat real estate developers and shady businessmen and mobsters. That is the arena Mr. Trump knows, and the one he respects.

The world sneers at strongmen like Mr. Kim, Mr. Putin and Rodrigo Duterte, the president of the Philippines, regarding them as uncivilized thugs, and Mr. Trump feels similarly disrespected. Dispositionally speaking, these are Mr. Trump’s people. As such, the president feels more confident and less defensive with these people than he does with leaders with whom, from a geopolitical perspective, he is on more equal footing. This is especially true of Mr. Kim, a global pariah from a devastatingly poor and dysfunctional nation to whom Mr. Trump can feel superior in every way.

Plus, Mr. Trump is way taller than Mr. Kim. And for this president, size does matter.

As for why Mr. Trump is so committed to tackling the North Korea tangle, there are a couple of key Trumpian impulses at play — beyond whatever concerns the president may have long harbored regarding nuclear proliferation, of course. Most simply, Mr. Trump loves a deal. Cutting big deals on his own is what he thought the presidency was going to be all about. The realization that he must contend with the squabbling foot-draggers in Congress has been a constant source of frustration to him on the domestic front. But on foreign policy, he has way more wiggle room to make his mark.

More tempting still, Mr. Trump loves big risks and long shots. He sees them as no-lose propositions: If he fails with North Korea, who can fault him, really? After all, it was an impossible mission, at which all his predecessors failed. In discussing his decision to trust Mr. Kim, Mr. Trump displayed an impressive dose of self-awareness on this point: “I may be wrong. I mean, I may stand before you in six months and say, ‘Hey, I was wrong.’ I don’t know that I’ll ever admit that, but I’ll find some kind of an excuse.”

But if he somehow can pull off this trick, boy oh boy, won’t everyone be amazed. This is ultimately what makes North Korea so irresistible to Mr. Trump. There are indeed lots of bad actors and dangerous regimes and looming threats on the world stage. But which regime is seen as the most unpredictable, the most isolated, the craziest of crazy? If Mr. Trump can crack this nut, he’ll surely get the adulation — not to mention the Nobel Peace Prize — that he is so desperate for.