Looks like you'd put your thumb inside the ring onto the point of the plunger, index and middle fingers on each side of the "butterfly." Press down to expose the flat head of the plunger, then slide it into the black base. Release, and the butterfly keeps the plunger head from sliding out of either side of the base.
So, the weight of the top would be suspended by the plunger and ring, x4. I think my main aim would be to make sure that each of your four lines pulls straight up, rather than tweaking any of these things at an angle. You may need to build a square frame (one line down from the hoist to the frame, four individual lines from the corners of the frame to each mount).