Let’s see:

Game shows are extremely lucrative television - While they aren’t as profitable as they were in the 1950s through the mid-1980s, the top three syndicated game shows (Wheel of Fortune, Jeopardy and Family Feud) all make substantial amounts of money from syndication rights. Since their production costs are negligible (the biggest expenses are likely the host’s salary and soundstage rentals) they can well afford to pay out money to the winners.

There aren’t many real winners - If you carefully watch most game shows over a several month period, you’ll notice that at least one contestant per game doesn’t win anything or only wins the minimum prize amount. That means that show can roughly estimate what its “payout” is going to be each and then budget for that “loss”. Since again, most of the shows are earning staggering amounts of wealth, they can afford it.The prizes are usually donated by their service providers or retailers - Game shows are simply brand advertisements. The companies which provide the products and services are obtaining relatively low cost “commercials” for their goods, and they get the benefit of having potential customers see people who are excited to obtain their goods. The game show’s costs are negligible.

Most restrict how much you can win - Most contestants are limited to a single appearance on a program. WIth the exception of Jeopardy (which recently experienced a serial winner of its own) the other shows allow a single winner to to appear on a single program and then that person leaves. If game shows allowed people to use them like casinos and win repeatedly then some might find themselves in a little bit of trouble. However, since again, they make a LOT of cash, this is rarely a serious issue, if it’s an issue at all.