Can a transformer have no secondary stages?
It's choke, a.k.a. an inductor. The nameplate says 125mH 6A.

From inspecting the wiring, only two power wires go to the spindle, so it's single-phase and the inductor is in series.

Its purpose is to limit the current that can flow to the spindle motor; this limits the torque the spindle motor can develop. It also much reduces the peak current to the spindle motor when starting or stalled.