The phrase "fishing minigame" refers to a small game within a larger video game where the player can participate in a fishing activity. Full definition
For some reason I love fishing minigames in games (especially Dark Cloud and Breath of Fire), it's a strange addiction. (blog.us.playstation.com)
The dungeons are procedurally generated; the room layout and configuration are random, as are the events, traps, puzzles, loot, and fishing minigames within. (darkstation.com)
It's good to see that when mecha games finally get their own fishing minigames, the fish are scaled up to the capabilities of the mecha. (mechadamashii.com)