Professional poker players also have a lot of other sources of income. Many of them are doing stuff like:
-writing a book on gambling or poker
-doing affiliate marketing on their website for a casino
-giving out premium picks on membership channels
-building their own casino and running that
We should not narrow down their sources of income as poker or sports betting as said. There is the this "cushion" of income to back them up and all these are the non-gambling modes of earning.
But what you've mentioned only comes after they've become a known figure in the poker circle and it's going to take a long time for that to happen to them because there's a lot of big fishes you've got to challenge and get through to make a name for yourself but that's not the best way to get famous in poker and make a living out of gambling, the best way would be for you to play other games like roulette, blackjack or baccarat and make a killing out of those games which is difficult to do given that those games that I've mentioned aren't that easy to play because it's chance based unlike poker. And to answer the question, yes you can make a living out of gambling but it's not for everyone so don't get your hopes up about it, just gamble for entertainment.