Do mechanisms always result in a series of strategic games being played out? Mechanism design is an offshoot of game theory, and many call it "inverse game theory", since it involves the use of incentives to ensure that the end result of the game being played out is beneficial to the designer of the game.

That being said, is it always the case that whenever a mechanism is implemented, it results in a game being played out amongst the players?

My intuition says "no", since no game will take place if it is the dominant strategy for all players to reveal their true preferences. Am I correct?
I'm not sure what you mean by "results in a game".

When doing mechanism design, after you've fixed a mechanism, the resulting mathematical structure can be identified with a game which we solve using the tools of game theory. That is, the choice of a mechanism induces a game. I suppose you could take this to mean that it results in a game.

Just because that game has dominant strategies does not mean the game doesn't "take place". In fact, I don't even know how you can speak of dominant strategies when you don't (even if only implicitly) have a game in mind when doing so.