Yes, it's a 3-phase set of motor windings. Designed to drive a specific magnet configuration which might not match your magnet as you don't say which way it is magnetised.
The three coils are connected in the middle, but in the original circuit the middle is not connected further to anything. I guess this is normal in 3 phase coiling. But since I have only a ULN2803A darlington array for this, I guess I have to power the coils in the middle (the blue line) and then sink the current through the ULN2803A.
Then I use PWM on pins 2, 3 and 4 to vary the magnetic field. By varying the PWM strength on each coil, I might get interesting effects on a magnetic or simply just an iron object on top of the coils, which would be the purpose of my project. In this circuit I can't reverse the current in the coils, only vary the strength of the magnetic field in one direction.