What is the meaning of "Nasachti"?
Radak: It is an expression of authority and grandeur, like "Nesichei Sichon" (Yehoshua 13:21), "Gam Eloheihem Im Nesicheihem" (Daniel 11:8). It is My king, that I anointed - "Ra'isi b'Vanav Li Melech" (Shmuel I, 16:1) - Li, for My service.
What is the meaning of "Malki"?
Radak: A king for My service. The word can also mean opposite - "vEi'lokim Malki mi'Kedem" (74:12), He is king over me. Suffixes that are pronouns [can be from either perspective] - "Haser me'Alai Nig'echa" (39:11), "mi'Neged Nig'i Ya'amodu" (38:12), "v'Simachtim b'Veis Tefilasi" (Yeshayah 56:7), "Shamati Es Tefilasecha" (Melachim I, 9:3).
Malbim: Refer to 2:7:4:3.
What is the content of Hashem's words?
Rashi: Why are you agitated? I appointed [David] to be king on Tziyon, My holy mountain!
Radak: How do they think to uproot the kingship from Beis David? I made him king!
Malbim: You are agitated to rebel. At this time that you thought to cast off the yoke of Malchus Beis David, I anointed My king. Through your rebellion will be revealed that I anointed him to rule over Tziyon, My holy mountain!
Was David king only over Tziyon?
Radak: Metzudas Tziyon was conquered only after David came to conquer it; after he conquered it, Pelishtim gathered to fight him.