Does the Quran encourage ill-treatment of non-Muslims?
The 'disbelievers' in this verse refers to those who persecuted and attacked the Muslims. This is not a verse directing Muslim to just go out and be awful to non-Muslims.
In fact there is a lot in the Quran and hadith collections that command Muslims to be compassionate and kind to all of God's creation. One such hadith states: Whoever is deprived of gentleness is deprived of all good. (Muslim, Abu Dawood)
It is also reported by Abu Dawood (a hadith collection) that Muhammad said, 'Beware! Whoever is cruel and hard on a non-Muslim minority, or curtails their rights, or burdens them with more than they can bear, or takes anything from them against their free will; I (Muhammad) will complain against the person on the Day of Judgement.'