However, the author does not "appear" to have the Luff Tackle variation. [1] I think it's close to the 6:1 variation on row two, except with the pulley directly attached to the ceiling.
The systematic approach seems to work, just appears to be missing a few combinations, or it was not really systematic. Such as, their should probably be a lot of pulley combinations that are basically "nothing", or "not helpful" combinations. 1:1, or 1/2:1, ect... combinations that just noted as discarded (or maybe curiosities that "might" have a use)
A 1:1 pulley is not "technically" significant from this perspective, yet it does change the force direction.
[1] https://en.wikipedia.org/wiki/Pulley#Method_of_operation