The comparison of his total net worth to the North Korea's yearly GDP and army size is irrelevant.
If he even tried to raise an army to resist the will of the US government, they would seize his assets so fast his head would spin.
That's not to say money doesn't buy political influence, but it's a much subtler kind of influence.
NK may not have that much worth in USD, but it occupies territory and has military force to back its claim, and that military is motivated by things other than USD numbers on computers somewhere.
If he had covertly planned ahead and already had his mercenary army in place maybe. (though maybe he'll have the secret code for all the drones....)
https://www.cnn.com/2019/10/31/americas/el-chapo-son-operati...
The difference in what's basically a warlord who already has loyal troops to command, controls territory, and assets that can't be easily seized and Jeff Bezos is too much to make a comparison remotely useful.
In abstract, from the numbers sense (dollars), sure, your argument stands that test.
However, it does not stand the common sense test: what are said contractors going to do once the gig is over? Part of mil contracting is keeping yourself in the good graces of the sugar-daddy government to keep the funds rolling into the future when needs arise. Oh yeah, and also avoid going to prison (for reference, see Blackwater / US Contractor indemnification in Iraq).
Billionaires are our kings. Jeff Bezos' wealth is 3 times the GDP of North Kora, which has a standing army of over a million people. They are more wealthy than a number of independent states. Do you think he couldn't fund and equip 100,000 mercenaries if his monopoly were threatened? When a peasant threatens his power, he doesn't even need to do that: a single assassin is enough. Replace Bezos (who I doubt would order a hit but you never know) with a Russian oligarch (who absolutely would order a hit) and you have your explanation.