Yes, it is possible to win real money through Hearthstone betting. You can indeed find some major sportsbooks that offer wagers for this Esport. However, being a niche genre, Hearthstone wagers are not so varied.
But first, you need to pick a sportsbook website that is legal in your country/state or seek an offshore one. You need to provide your identification and proof of income to register on most reputed sportsbooks websites to register an account.
The legal age for gambling can vary depending on the laws of where you live. Pretty much every sportsbook website will have a minimum age limit requirement of 18 years, if not 21.