Quick Games

Does playing short games help you improve your chess skills? These chess skills I'm referring to doesn't include being able to move the pieces faster with better precision. 

Any chess practice can improve your chess skills. It all depends on what you do with the games. If you are just playing then you will probably not get a ton of benefit. However, if you go over your games, even briefly, and see where you missed things (such as deviating from book or known theory or missed tactical shots/mates) then you can use that to help guide study.

yep. as long as you analyze the games afterwards. lets say you play 5 blitz games, and then you analyze them trying to find some error you made, like making a wrong plan, or missing tactical oppurtunities, or playing wrong in different times of the game, like endgame or opening. then you have to eliminate these errors.