Yes, this part is responsible forward/reverse play . When you press play it should be tilting either side. I just finished working on mine WM-GX670, and this looks very much the same mechanically.
@BusiG Watched the video, can't hear the solenoid. Right after you press play, the solenoid should engage (pressing play not shown in the video). Does it do that ? Ideally you should remove the PCB and engage the mechanism by hand to see exactly what happens. A broken clutch gear can be a problem on these units.
This is how the mech looks like under PSB.i removed clutch gear for repairs but it opens up the view of the internal mechanics. I hope this helps you in some ways
