do game animals have poor eyesight?
These species likely don't see you as a predator, or if they do they don't know if you've seen them yet.

A study indicated that the vision of the White-tailed deer was good; 


  As expected for a crepuscularly active prey species, the visual system of white-tailed deer is specialized for sensitivity in low-light conditions and detection of predators.


The observation that many prey species only notice movement may relate to behavioural adaptations that increase their chances against natural predator species. Staying still while monitoring your surrounds decreases the chance of the predator seeing you.
I'll quote D'Angelo et al again; 


  The visual streak of deer in combination with
  their wide-set eyes likely provides them with enhanced ability
  to monitor the horizon and to detect movement with a
  wide field of view while keeping their head stationary.


Visual specialization of an herbivore prey species, the white-tailed deer.
G. J. D’Angelo, A. Glasser, M. Wendt, G. A. Williams, D. A. Osborn, G. R. Gallagher, R. J. Warren, K. V. Miller, M. T. Pardue
Canadian Journal of Zoology, 2008, 86:735-743, 10.1139/Z08-050