I think you have not done up that ring thingy beside the crank arm. It has a small allen bolt, loosen that and you should be able to twist the ring towards the BB which should remove the gap.
He can't see the threads on the axle because they are on the arms.
And looking at his photo, I suspect that the ring is done up all towards the arm side hence the space between the arm and bb and not the lack of spacers for the BB.
I think you have not done up that ring thingy beside the crank arm. It has a small allen bolt, loosen that and you should be able to twist the ring towards the BB which should remove the gap.