The first definition is better as it defines the institution of government. The second is not so good because a government does more than make laws (the legislative role). It also has executive and judicial roles.
Islam was very impact on the medieval society of Europe due to its golden age. Europeans translated Arabic works on things like alchemy, astronomy, mathematics, science in general, medicine, arts, and numerous other aspects of culture that we now take for granted without even realizing how big they were at the time that the Arabic scholars discovered them.<span />