They will say, "Did there not come to you your messengers with clear proofs?" They will say, "Yes." They will reply, "Then supplicate [yourselves], but the supplication (dua) of the disbelievers is not except in error."
The truth is that this Verse is in regards to the dua of the kaafir on the Day of Judgment. In this world, when a kaafir makes dua for something or seeks it from Allaah, there is the effect of his dua as many Verses of the Qur'aan attest to that.
As for the question as to if this can be termed an answer to his dua or not, then that question has no benefit (i.e. it is useless).
Ibn al-Qayyim said:
Allaah is not pleased with every person whose dua He answers. Neither does He love every such person. Nor is He pleased with his actions. For indeed, Allaah answers the dua of the pious, evil, believer, and kaafir.
Ibn Taymiyyah said:
The entire creation makes dua to Allaah. This includes the believers and kaafirs among the creation. Allaah answers the dua of the kuffaar. Indeed, the kuffaar ask Allaah to feed them. So, He feeds them and gives them to drink. And when distress touches them in the ocean (when they travel in it), then the one who calls upon anyone but Him has gone astray. When He delivers them to the land (by answering their dua) they turn away. And humans are so ungrateful.
He also said:
As for answering those who ask, then that encompasses everyone. Allaah, indeed, answers the dua of the one who is in distress and the one who has been wronged even if he be a kaafir.