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....because Gates gives his money to his foundation (lowering his net worth) and Bezos doesn't.
The article says "Gates is only other person to have built 13-figure fortune" but isn't $100B a 12-figure fortune? I suggested we count zeros instead which would make Bezos a level 11 and Gates a high level 10: http://www.kmeme.com/2017/11/the-richer-scale.html
Measuring paper wealth is an exercise in too many assumptions. It doesn't take into effect any exogenous factors such as interest rates, and depends upon a vast, fragile edifice to protect his property rights--there are probably 100,000 people protecting his net worth.
Measuring paper wealth in such an exceptionally massive, highly liquid market with such a long track-record, is extremely easy in fact. It requires few assumptions.

There's absolutely nothing fragile about what's protecting his property rights.

Quite the opposite. It has endured for hundreds of years while the most of the rest of the world has constantly failed and been remade by war, famine, poverty, social collapse, political upheaval and shifting borders.

What political structure or arrangement would you name from the last thousand years or so that has endured better or longer exactly? There are few.