If we're talking video games, and how they can be modeled/ported to tabletop, then the fundamental difference between a cover based shooter and a more traditional one is that the cover based shooter lets you shoot "blind" from behind total cover without exposing yourself (much) to return fire. To replicate that in a tabletop game, all you need is that ability. It could be a feat, trick, campaign quality, or a variety of other things, along the lines of:
When you are in total cover, you are still able to track the locations of characters behind the cover, and may make attacks against them with 1-handed ranged weapons without leaving your cover. You suffer penalties with this attack as though the target were invisible, but you do not need to guess their location.
For the ability to dash between cover objects quickly without presenting much of a target, that's already covered by the nature of turn based combat. You only move on your turn, and you tend not to get shot at on your turn*. Everything else is just narrative. Do you imagine your character hugging the wall and advancing in tom-clancy-tactical fashion, or do you imagine your character calmly walking the end of the wall while reloading his gun like a boss, or clint eastwood.
*exceptions apply, see store for details