I had to look that quote up to fully understand it, plus find the clip online, so here is the context:
https://www.youtube.com/watch?v=AtoM9x-Bfu8
Omar robs drug kingpin Marlo who is at a card night, sat round the table, raking in winnings. Marlo claims the money is his, in response Omar says “Man, money ain’t got no owners, only spenders.” He then goes on to take Marlo's ring rather than just run off with the $$$.
So, in the context of the show, Marlo thinks he has just raked in all of these chips and made himself rich, there is the stack of these bits of plastic chips in front of him.
Meanwhile, the $$$ gets handed to Omar straight from where it is kept in the back of the room, the 'bank' off table. All the money for all the chips that are on the table is kept in this one area that Omar is able to head off with, leaving Marlo with his useless chips on the table. At the instant that Omar takes the money all the chips on the table are rendered useless for all players and no longer of value. It is apparent for all that the chips will not be exchanged for USD at the 'bank'.
Marlo doesn't just lose the 'fiat' $$$ that he thought he was winning, he also loses the ring on his finger. Although the money may be just money and he may not have lost as much as the prize pot, the ring is an item that cannot be so easily replaced. It has value beyond nominal gold value, sentimental value.
Before Omar rocks up the card game is being played in an unregulated way with the players having to trust but verify each other. Nobody cheats at the game. The card deck has its own blockchain technology.
The Wire was a long time ago and now Omar has realised that it is more lucrative to move into crypto. So in the 2018 remake Omar does not need a gun to steal all the money from all of the gamblers using a set of chips. He uses chips he printed earlier and limits the available chips so new players wanting to win big in the unregulated card game have to pay more for their chips.
Not all players play every game, most just hold on to their chips hoping others wanting to play will want to buy their chips. So they tell others to play the game. The value of their chips goes up so notionally the chips are now worth millions even though there is only a huge but nonetheless smaller pile of money in the 'bank'.
Because any one player can cash out at any time they do not care if there is less than the sum total of all play money in the 'bank'. So long as there is a multiple of what their chips are worth they have no real concern, unless everyone else starts cashing out.
Because the bank is quite slow and everyone has to queue, some players start to sell their own tokens. These can be placed as side bets on the major games. These coins are copies of the original coins but are super lightweight and have an alleged advantage of being totally anonymous, nobody can track them.
Some of these players are making good business on this side betting and they tell their customers that their coins will one day be able to be useful for more things than side bets. One day they will be able to do every day things with the tokens like get a shopping trolley at a supermarket with one, thereby not needing a 'fiat currency coin'.
So Omar rocks up and rather than use a gun he simply takes his position on the coin to run off with all the money. The people with the chips thought they were the lucky ones owning all the money but no, Omar goes and spends it for them.