"Allah does not listen so attentively" has two- fold meanings. First, Allah's acceptance and pleasure. Second, His attribute of Hearing. One must have to believe in it although we can neither describe it nor compare it with anything else.
The word "Ghina" is ordinarily used for singing but here it means the recitation which is done in accordance with the principles of Tajwid and in a beautiful voice.
Thus, this Hadith induces us to recite the Qur'an properly with nice feeling and voice.