The answer is that what is meant by “prayer” here is an act of the same order as reciting the Qur’an, as has already been explained. This very verse obliges anyone to whom the Qur’an is recited to prostrate. If the recitation reaches him while he is outside the ṣalāh, he must prostrate soon thereafter, once the time for one of the obligatory prayers comes in—for there is no moment in which the Qur’an is read to him except that it coincides with the time of a prescribed prayer, and the gap between him and that prayer is always less than half a day. Should he fail to perform that prayer, he becomes one of those who, when the Qur’an is recited to them, do not prostrate.
If the Qur’an is recited to him during the ṣalāh, he must make one sujūd in which he descends from the standing position and another in which he descends from the sitting position, each of them coming after rukūʿ, exactly as the Messenger of Allah ﷺ demonstrated.
As for the prostration triggered by the recitation of this very verse, that is the specific act known as sujūd al-tilāwah. One hastens to it the moment he hears the verse, for the verse itself commands him to prostrate whenever the Qur’an is recited to him; perfect promptness therefore dictates that he perform sujūd al-tilāwah as soon as he hears it. He then prostrates at the recitation of other verses as outlined earlier, for this verse commands prostration whether it or some other passage is recited. It is the verse that enjoins prostration upon the recitation of the Qur’an, unlike the rest of the passages at which no sujūd is prescribed. Accordingly, it possesses a special claim to that command while still being part of the Qur’an as a whole: it is singled out for its own prostration, and the worshipper prostrates when it is recited during prayer just as he prostrates when any other verse that calls for sujūd is recited.