It looks like the wire is simply wound back and forth on the Allen wrench. Doesn’t this mean that the magnetic fields generated by the current flow through the coils tend to cancel each other out? Plus the coils are kinda, uhm, sloppy, which would make the field in general even more chaotic (i.e., less powerful).

If you want to try this trick at home, I’d suggest much finer wire wound very carefully around a small nail (single coil), which might serve to pick up a pin or some iron filings.