All games use mechanics; however, theories and styles differ as to their ultimate importance to the game.
Other games which use similar mechanics are also included in this category.
For very large systems, the relative total energies can be compared using molecular mechanics.
In modern chemistry this is derived using statistical mechanics.
"It was almost like they were using mechanics."
One would need to use statistical mechanics to do what you have in mind, which is considerably more complex.
Several games use mechanics that allow one or more dice to be rerolled, with each successive roll being added to the total.
The relation of the one continuum to the other is not possible using Newtonian mechanics.
The game uses several mechanics (primarily radiation) which act as barriers.
Mechanical engineers typically use mechanics in the design or analysis phases of engineering.