3 Card Poker has only been around since the mid-90s, when a card enthusiast called Derek Webb first created and patented the game, which he intended to sell to Casinos on both sides of the Atlantic.
There was lawsuits, involving the likes of PGIC who owned the somewhat similar Caribbean Stud Poker and argued that Three-Card Poker had ripped off their game. But the game was rapidly becoming a staple of land-based Casinos, who liked the quick turnover of games, played at roughly the same pace as the likes of Blackjack. Card players liked it, too. The rules are simple, the strategy side of things never gets too complex, and the possibility of a big payout, thanks to a strong hand is always there.
It was therefore somewhat inevitable that online casinos started adopting it, as well. Fans of table games and those who enjoy playing other forms of Poker should take a shine to it, too.