Maybe they expect a highscore board.

I get it but also, what if they don't care about being rich when they're dead?
What if they only care about being rich when they're alive?
What if they care less about having money, and more about having the power that money can bring - and using that power to influence the world they (for now) and their offspring (in the future) live in.
I think "you can't take it with you" stops applying to people obsessed with legacy.
- This is why I'm pointing out in this thread that their "legacy" doesn't last for longer than a couple of decades at best.
  
  I think legacy certainly can last longer than a few decades. Intergenerational wealth, while absolutely often squandered by the third generation (I've heard), is proof that legacy can live on. There are estate houses in the UK that are hundreds of years old, I think that's a sort of legacy that has survived.
  I don't disagree with you that it's ultimately very petty but legacy certainly can outlast a few decades. And even if it doesn't -- if the ultra-wealthy person in question believes they can make their legacy last forever, that'll be why they're hoarding.

Not a perfect argument, because we probably only know about the richest Sumerians because they could afford burial tombs and stone carvings to tell their stories. Likewise, the world will long remember Elon Musk and Warren Buffett because they have used their wealth to build monuments to themselves, metaphorically speaking of course. Rich people are always paying money to name shit after themselves, and in that way they get to live on and be remembered. Even gravestones vary in quality and longevity, and a pauper's grave is only marked by the flowers that grow there.
People who hoard wealth don't believe the adage that "no amount of money ever bought a minute of time." In fact, they probably know it isn't true. They pay to have someone do their laundry and their dishes. They pay for private jets to leave when they are ready and go directly where they want to go. A rich person doesn't wait for a bus that's running late, or a boss that has other priorities. A rich person has healthcare appointments and all the therapies and drugs that extend and improve the quality of their lives.
They buy time all the time. And the more you have at the end, the more valuable your end becomes. Then it's a competition to see who can impress you most and receive the largest bequest. Which of your children will change your diapers? Which of your charities will build the biggest monument to your name? What final experiences and celebrations and sights can distract you from your impending doom?
Oblivion severs all ties and eliminates all consequences. You can't take it with you, but why would you care? You aren't taking you with you. You is over, and there is no "with you" to take anything. The moment of death is the only moment when you can in fact have your cake and eat it, too, because that moment is the entirety of your life experience. It is everything, and the next moment is nothing. And your point total at the end can dramatically alter the quality of that eternal moment.
- Historians and a few enthusiasts might know the names of some rich Sumerians (and for Sumerians, many might remember just as well the name of a merchant on some impressively well-preserved tablet), maybe, but that's even a very small amount of historians anyway. Most people won't even be able to tell you the name of the Pharaoh who built the most impressive pyramid, nevermind about all the rest of them!
  Nobody except a few weirdos remembers this shite after a couple thousand millenia! And it definitelly doesn't matter whatsoever. Musks and Bezos' won't even be remembered 500 years from now, nevermind 4000.
  
  Honestly, the first name I thought of was Conan the Barbarian, but he was Cimmerian, not Sumerian. But if anyone knows any Sumerians, it's because they were rich or important.
  People of great importance are also remembered. Great scientists and artists and leaders are remembered for their contributions. But if you are not a great person, then being rich will let you buy fame.
  Musk and Bezos will be remembered for their atrocities as much as for their wealth, but Bezos spent $42 million building a 10,000 year clock and Musk launched one of his cars into space. These guys may or may bot succeed, but they are trying to buy an indelible legacy. If all of modern humanity is lost, and remnants are discovered 10,001 years in the future, there will be far more evidence that Musk and Bezos were here than you or I, and that's not because they are good people or important people. It's because they are rich.

They know they can’t take it with them. That’s not the point. They derive joy from denying others.
Some people can’t enjoy what they have, unless they know someone else has less. And unfortunately, this world elevates those sociopaths to the top.