The same contrast is very clear here:
Psalm 90:2
Before the mountains were born or you brought forth the earth and the world, from everlasting to everlasting you are God.
πρὸ τοῦ ὄρη γενηθῆναι καὶ πλασθῆναι τὴν γῆν καὶ τὴν οἰκουμένην καὶ ἀπὸ τοῦ αἰῶνος ἕως τοῦ αἰῶνος σὺ εἶ
Note how "eimi" is used absolutely here too: σὺ εἶ (You are God)
It's actually similar to:
John 8:58
I tell you the truth, Jesus answered, "before Abraham was born, I am!"
εἶπεν αὐτοῖς Ἰησοῦς· ἀμὴν ἀμὴν λέγω ὑμῖν, πρὶν Ἀβραὰμ γενέσθαι ἐγὼ εἰμί
σὺ εἶ: you are (You are God)
ἐγὼ εἰμί: I am
The same verb ειμι, Present active indicative.
So by comparison, not only does it mean "I am", it means "I am God"