Wealth may be denominated in dollars, but that doesn't mean you have to hold dollars to have wealth.
If I have $1M and use it all to buy a house, does that now mean I am worth 0?
Also, imagine there are 100 total shares of a company that were bought for $10 each. If the next time somebody trades a share and it is for $100, that would be the value for all 99 other shares. That is how market cap of a company is calculated. It's also how people like Mark Zuckerberg and Bill Gates are worth 10's of billions of dollars, without actually having it in the bank. They didn't necessarily gain all their wealth by taking it away from other people.