Mostly these very large purchases, such as extra large boats, would be done through trusts, companies and combinations of the two, and in various jurisdictions.
And when it comes to making payment the individual would most likely simply instruct their family office or private banker to make it happen, and assume it would be done in a way that is tax efficient, opaque to outsiders and, hopefully, legal.
Article has very little information on the subject. AFAIK, you will be fool to pay for $100M jet using cash, credit or check the way article seems to suggest. Most of these purchases are done by taking out a loan. Typically high networth individual can earn far more on $100M than typical loan rates. Often, such assets would be put in to some LLC or made part of their businesses where the use of the asset can be put as compensation or business expense. A real estate can even be declared as rental business where you use it may be for a month and rest of the time it’s generating losses that can be used for taxes. Interest payments, depriciation, conceived losses in this “business” goes long way for favorable tax treatment.
My understanding is that yachts are owned by a company whose 'investor' keeps having to bail it out. "Oh dear" cries the billionaire to their accountant "such an enormous tax loss". Of course, the occasional week long rental to mere multi-millionaires does help fill the hole a little.