Does this verse imply that Islam should be imposed militarily?
Answer
The key to understanding such a Quranic verse which speaks of fighting is to read it within its surrounding passage and appreciate which enemy was being spoken of in the context of its revelation. Here in Surat al-Baqarah (read 2:190-193 together), permission was given, or reiterated, to fight against the idolaters who had driven the Muslims out of Makkah, forcing some of them to migrate to Abyssinia (modern-day Ethiopia) and later to the city of Yathrib, which was renamed to Madinah.
The clearest meaning of fitnah (tribulation) in this verse, as the endpoint of hostilities, is that it refers to the efforts of the idolatrous Makkans to force Muslims to give up their faith. Al-Bukhari reports that Ibn ‘Umar said, “We did so (i.e. fought until there was no more fitnah) in the time of Allah’s Messenger, Muhammad ﷺ. A man would be tested (yuftanu) in his religion: either they would kill him or torture him. Then, when Islam became widespread, there was no longer tribulation (fitnah).”
Furthermore, the conclusion of the verse “Let there be no hostility except against the wrongdoers” has been explained by a number of commentators to mean that only those of them who fight against you should be fought.
Summary
This verse was revealed to urge Muslims to fight those who had persecuted them for their faith.