A creature with double strike deals both first strike and normal combat damage. For instance, a 1/2 creature with double strike such as Boros Swiftblade would defeat a 2/1 creature in combat and survive, due to destroying it with first strike damage. It would also destroy a 2/2 creature, though be destroyed itself because the opposing creature survived the first strike to deal its own damage.
So its pretty straightforward, its precisely what it sounds like. This creature with double strike is quick enough to not only hit before others but hit twice in the time it takes most opponents to hit once.
For This one we follow the spirit of multiple-strikes and quick attacks instead of hte letter of double. A game in which after you attack enemies you have a brief window in time to attack again before they can re-cover. The more attacks in a row you have the shorter the window gets and if you try to attack again and fail you lose balance and leave yourself vulnerable. Bring rhythm games into the action game arena.
Of course you would be a bit weaker relative to your enemies compared to other games. I am thinking of something akin to the thief series. Your window for making new attacks would be based on your attack animations so its not arbitrary button timing or a quick-time-event. I envision a time-slow effect when you make the first strike and it slowly wearing off as you make subsequent strikes for the visuals.