"From what i could see there is part A and part B. If you watch closely a woman is assembling 2 different parts in spite of the vid only showing one type of cut op. One of the parts has the large flange bent upward along the equator to afford alignment between he two halves and an opportunity for the adhesive to wick upward to the OUTSIDE of the sphere form. This would deter adhesive from flowing into the sphere and puts all of the access on the outside of the ball. The upward bent flange could be removed with a lathe operation without too much fuss , much like the trimming op seen in the vid.  The assembly process is clever in that it puts any excess materials (flange/adhesive) on the outside of the sphere for later removal.  IIRC ping pong balls have a very light texture so its a safe bet that after the cut away of the flange and excess adhesive its textured with a sand blast like process, this would erase any vestiges of the last cutting process."