Praise be to Allah, and may peace and blessings be upon the Messenger of Allah.
This question is based on an incorrect understanding. A disbeliever is addressed by the rulings of Islamic law, even if he does not abide by them in this world, and therefore he will be held accountable for them on the Day of Resurrection.
Allah تعالى says, describing the people of Hell:
“What has landed you in Saqar? They will say, ‘We were not among those who prayed, nor did we feed the needy, and we used to indulge in vain discourse with those who did so, and we used to deny the Day of Judgment.’” [Al-Muddaththir: 42–46]
This indicates that they were punished for abandoning prayer and failing to feed those in need, in addition to their denial of the Day of Judgment.
A disbeliever is also held accountable for the blessings Allah bestowed upon him and for which he did not show gratitude. Allah تعالى says:
“There is no blame upon those who believe and do righteous deeds concerning what they consumed.” [Al-Ma'idah: 93]
And He سبحانه says:
“Say: ‘They are for those who believe during the worldly life, exclusively for them on the Day of Resurrection.’” [Al-A'raf: 32]
Therefore, the disbeliever will be held accountable on the Day of Resurrection for his disbelief, his deeds, and the obligations he neglected, but his reckoning differs from that of the believer.
A believer may undergo an easy reckoning, in which his sins are brought before him, then Allah conceals them and forgives him. As for the disbeliever, he will be exposed for his sins before all creation and humiliated because of them, as Allah تعالى says:
“And the witnesses will say, ‘These are the ones who lied about their Lord. Surely, the curse of Allah is upon the wrongdoers.’” [Hud: 18]
And Allah knows best.