Does the remembrance (dhikr) that distances one from this world and brings one closer to the Hereafter mean that it shortens one's life?

What you mentioned, that remembrance (dhikr) distances one from this world and draws one closer to the Hereafter, is not a Prophetic Hadith. Rather, it is the meaning of the words of some scholars. It means that dhikr makes a person ascetic regarding this world and increases his contentment, which shortens his worldly hopes and increases his zeal to work for the Hereafter. These meanings are realized if the dhikr of the heart aligns with the dhikr of the tongue.