Yes, when designed right.
The Mini games are designed to introduce meaningful choices for champs, while implementing Counter play to there kits.
It seems like a discussion about the new champs. But everyone's favorite executioner had a juggling minigame long before minigames were cool.
But where mini game design goes wrong, can sometime lie in the Execution. Fiora's vitals seem like a good idea, but if she can proc them too reliably, then it doesn't really add significant counterplay. (And we know it doesn't have a counter build either.) The other problem, which is more of a health problem than a counterplay problem. If a champion's mini game becomes so Obtuse that player's go "We didn't sign up for this." Which is a main case for Global minigames such as Skarner's passive. Or Illaoi, Her mini game has tons of counterplay, (kill the tentacles) but doing that, along side with interacting with the Spirit, is what people really hate.