Will Allah Almighty compensate in the Hereafter the disbeliever who lived in this world in hardship and poverty and died upon that, by virtue of Allah Almighty's justice?

The one who benefits from calamities in an otherworldly way is only the believer, as stated in the Prophet's (peace and blessings be upon him) hadith: "Wondrous is the affair of the believer, for all his affairs are good." As for non-believers, their calamities do not expiate their sins, but their degrees of torment in Hellfire vary according to their deeds. Disbelievers differ in their disbelief, and whoever's disbelief is less severe due to their support for Muslims might have their torment lightened, as happened to Abu Talib. Calamities might also deter some disbelievers from further corruption, resulting in a lighter punishment for them, while they might increase others in disbelief and criminality, leading to a more severe torment for them.