All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
The Prophet, sallallaahu ‘alayhi wa sallam, told us that when the soul is taken out of the body, the eyes follow it. [Ahmad and Muslim] This narration the soul can be seen, as the questioner quoted from Shaykh Ibn ‘Uthaymeen. This is the opinion of Ahlus-Sunnah.
Therefore, we believe that the soul can be seen, as mentioned in the narration, and that the dying person sees his soul leaving his body, so that he knows where it goes. However, we do not know how this sighting happens or for how long it lasts, because it is beyond our human perception. This is the case with the matters of the Hereafter and what takes place before it (i.e. death). However, we must believe in what Allaah and the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, told us about theses matters, because this will save us from erring.
Also note the Quranic verse (which means): {And they ask you, [O Muhammad], about the soul. Say, "The soul is of the affair of my Lord. And mankind have not been given of knowledge except a little}[Quran 17:85] Only Allaah Knows the reality of the soul and the other matters that are related to it. In other words, the twenty-first century man does not know more about the soul than the Stone Age man. Allaah keeps this unknown to humans until the Day of Judgment.
Allaah Knows best.