The context of this verse was when the Muslims were to fight their enemies for their very existence. When the prophet Muhammad was receiving revelations from God at that point in time, he was being told about plans by the 'nonbeliever' (Pagan) regimes that dominated the area of Mecca at the time to murder him, his followers, and the messages he was trying to preach. He constructed the first Islamic village in Medina, northern modern-day Saudi Arabia, erecting the first mosque-- because he was booted out of his hometown, and there were nonstop excursions trying to murder him and his subjects. After thirteen years of endurance and patience, the prophet and his companions had to leave their home town of Mecca and to emigrate to Medina. When the people of Medina had welcomed him there and he was accepted as a leader there, the Meccans became unhappy. They wanted to eliminate Muhammad and his religion; and so they sent their army to root out Islam. And the crucial battle took place in Badr. It was just before this that Muhammad received the revelation from God to fight:
{And fight in the way of Allah with those who fight with you, and do not exceed the limits, surely Allah does not love those who exceed the limits.} (Al-Baqarah 2:190)
All religious revelations are contextual. The very tenet of Islam to avoid the consumption of alcohol itself was contextual-- as the revelations from God to Muhammad continued, the strictness surrounding the avoidance of its consumption strengthened.
Even the translation "nonbeliever" is translated more commonly to "Pagan", cuz that's technically more correct. Here's the entire verse surrounding the "slay the unbeliever"-- remember, this was revealed in the middle of the conflict between the two.
9:5-6 But when the forbidden months are past, then fight and slay the Pagans wherever ye find them, an seize them, beleaguer them, and lie in wait for them in every stratagem (of war); but if they repent, and establish regular prayers and practise regular charity, then open the way for them: for Allah is Oft-forgiving, Most Merciful. If one amongst the Pagans ask thee for asylum, grant it to him, so that he may hear the word of Allah. and then escort him to where he can be secure. That is because they are men without knowledge.
--
In other words, if they stop, they were to tell them of the message of God, and escorted to their own lands, and left to do as they please. This is why context is so important, and why buzzwords are so harmful to discussion.