That mass corresponds to "resistance to change" seems fairly natural, as does the correspondence between "pressure to change" and impulse. The strange part seems to be the correspondence between "strategy" and velocity.'' Distance would be something like strategy * time.

Does a symmetry in time correspond to a conservation of energy? Is energy supposed to correspond to resistance? Maybe, though that's a little hard to interpret, so it's a little difficult to apply Lagrangian or Hamiltonian mechanics. The interpretation of energy is important. Without that, the interpretation of time is incomplete and possibly incoherent.

Is there an inverse correspondence between optimal certainty in resistance * strategy (momentum) and optimal certainty in strategy * time (distance)? I guess, so findings from quantum uncertainty principles and information geometry may apply.

Does strategy impact one's perception of "distances" (strategy * time) and timescales? Maybe, so maybe findings from special relativity would apply. A universally-observable distance isn't defined though, and that precludes a more coherent application of special/general relativity. Some universal observables should be stated. Other than the obvious objectivity benefits, this could help more clearly define relationships between variables of different dimensions. This one isn't that important, but it would enable much more interesting uses of the theory.

I don't think that's a good way to think about it. More pressure doesn't always lead to more chance. It's about applying the right amount of pressure at the right point at the right time.

I don't see how your comment contradicts the part you quoted. More pressure doesn't lead to more change (in strategy) if resistance increases as well. That's consistent with what /u/SquirrelInHell stated.