“the Spirit.” “The Spirit” occurs in Ezekiel 1, here in Ezekiel 1:12, and later in Ezekiel 1:20. We later learn that the Spirit is Yahweh (Ezek. 8:2). God appears as “the Spirit” in Ezekiel 1:12, 20; 2:2; 3:12, 14, 24; 8:3; 11:1, 24). See commentary on Ezekiel 1:12 and 8:3.
“for the spirit of the living creature was in the wheels.” What the phrase means is unclear. Scholars do mostly agree that the phrase serves to show that the whole chariot-throne system works and moves together in concert.