David said that his prayer was sacrifice. Did he explicitly said that ALL prayer was sacrifice? No, but where in Scripture is it stated (or can be reasonably inferred) that there is a class of prayer that isn't sacrifice? You would agree that sacrifice can only be offered to God, right? You would agree that sacrifice offered is worship, right?
In his prayer recorded there in Psalm 103, David is talking directly to God's angels, exhorting them to "bless the Lord". His prayer at that point is specifically directed to angels, fellow created beings.
Using your tools of exegesis, David must be praying to his own soul in verses 1, 2, and 22 exhorting it to bless the Lord. In verse 22, is David praying to all God's works to bless the Lord? The structure of all five verses is the same - how can you justify translating two of them differently?
In the Book of Revelation, incense is used in the heavenly worship before the throne of God:
“Another angel came in holding a censer of gold. He took his place at the altar of incense and was given large amounts of incense to deposit on the altar of gold in front of the throne, together with the prayers of all God’s holy ones. From the angel’s hand, the smoke of the incense went up before God, and with it the prayers of God’s people.”
From the Book of Revelation
Revelation, chapter 8
CHAPTER 8*
3Another angel came and stood at the altar,* holding a gold censer. He was given a great quantity of incense to offer, along with the prayers of all the holy ones, on the gold altar that was before the throne.c
4The smoke of the incense along with the prayers of the holy ones went up before God from the hand of the angel.