When did his Nefesh cling to the earth?
Radak: It is when he was in danger and fled Avshalom, and he was close to death. It is as if his Nefesh clung to the earth.
Malbim: This refers to his request "Gemal Al Avdecha Echyeh" (17). Even though You granted to me physical life, my Nefesh is dead and buried in earth of the body, i.e. it is drawn after its desires.
Why does it say "Chayeni ki'Devarecha"?
Rashi: This is like You promised to me good via Nasan ha'Navi [Radak - "Ki Yimle'u Yamecha v'Shachavta Es Avosecha" (Shmuel II, 7:12).
Radak: You said in Your Torah "Ani Amis va'Achayeh."
Malbim: I should live life of the Nefesh in Avodas Hashem, like Your word in Torah "u'Vacharta ba'Chayim" (Devarim 30:19), i.e. life of the Nefesh.
