There are four mini-games: Blackjack, Dominoes, Five Finger Fillet, and Poker. You only need to start playing all of them for a moment to get the "Hobby Horse" trophy. You do not need to win, or even finish the match. After sitting down for a game, you can simply stand up again and leave. You can keep track of this at the pause menu under "Progress" - "Total Completion" - "Table Games". The mini-games can be found at the following locations.

Blackjack: Found in Rhodes (Saloon)
Dominoes: Found in Saint Denis (Park)
Five Finger Fillet: Found in Strawberry
Poker: Found in Saint Denis (Saloon)