More space on laptop [closed]
You certainly should be able to run a game from an external hard drive. Depending on how good of a hard drive you get, it may load the game slower or maybe even faster, but it should be able to play it. You will also be limited to the speed at which the data can be transferred over the connection (likely a USB).
If you plan on downloading the game via Steam, checkout this question on how to create a Steam Library on another drive. It's fairly simple, and will be necessary if you get your game from here.