Using the broomstick method you don't need to exert a huge amount of force - you bend over with the chook then you straighten up. I have done this with large gees as wells as chooks, ducks etc and never once had a less than instant kill. The only 'danger' is pulling too hard, if anything , and pulling the bird's head right off, which can be very messy if you then let go and it flaps about with blood spraying. But there is definitely no question of whether or not it is dead.
I would always recommend the broomstick method to someone despatching their first bird or nervous about the operation.
BTW in that YouTube video is it just me or does using a spanner about 5" long seem an unusually fiddly way of doing it?