Nobody's ever really agreed on what a game mechanic is.
If you zip around the web looking for an agreed definition, you'll come across a variety from the physical what-you-do actions that players take, to the loop of action and reaction and rules, to (in some cases) an attempt to express the more ephemeral sense of experience that a game can evoke.
The reason for this confusion is that the term game mechanic is lifted from the world of board games and tabletop role playing games, where it means moves and dice rolls.
Video games are very different from trad (or analog if you prefer) games in two important respects: Firstly, real time is a factor in the vast majority of them. Secondly, economy of information is a major factor because of the restrictive nature of the screen environment.
The upshot is that, like sports, video games are dynamic rather than mechanic driven. The rules are implicit and simple rather than explicit and complex. It makes sense to describe and think of them in loops and dynamics with predictable and outlier effects than action-and-rule mechanics, because much of the fun of them comes from the slightly chaotic, player-discovered patterns of play rather than formal strategy.
Rocket jumps, for example, are an effect of a dynamic environment, not any one deliberately designed mechanism. Any description of game design needs to be able to capture that chaos, don't you think?