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I've assumed the private talk Trump and Kim had went something like this:

Trump: There are 2 ways we can leave this meeting
1) We can be friends. I want to be best friends. If we are friends I will get NK more investment money than you know what to do with. I will use my contacts from business and as president to build NK as quick as possible. My country and the world will only let us be friends if you commit to complete verifiable denuclearization on my schedule.
-or-
2) We leave this room and say the time isn't right yet. Our people will keep talking and we'll meet again when we are ready.

I'm happy either way. What do you want? I probably don't need to mention it, but if you say you are ready to denuke (option 1) then you screw me, I will be the worst enemy you can imagine and I have the entire US military to help and the world won't stop it. So pick option 2 unless you're serious in your commitment now - I won't have any hard feelings unless you lie to me. We can get back to option 1 or something else when we're ready, but today these are the only two options I can commit to.

Kim: I WANT TO DENUKE.

Kim had a way out (option 2). It wasn't just a threat that made him agree - negotiations could continue if Kim wasn't ready. But, if Kim committed (option 1), he should consider his life (or at least his reign) over if he goes back on it. That's why Trump could feel confident when he got a commitment (it wasn't coerced as it would have been without option 2). The selling point for Kim was to a large degree INVESTMENTs in NK and Trump is going to make sure that goes smoothly no matter where the investments come from.

The people attacking Trump still don't have a clue how he makes deals. The safe "way out" (option 2) is critical to that meeting and for Trump to have confidence in any commitment. The threat is about stabbing Trump in the back, not about forcing denuclearization. Trump probably did it in a better way than the example above. But he can be confident in Kim's commitment, and from the movie and a few other things I'd bet Trump's "offer" was investments and building, not simply easing sanctions and being nice.