OK, I confess to only skim reading it
I didn't think it would be the chloride because milk already has up to 8.6g per gallon free chloride in it (mainly from salt) so adding 0.5g more is unlikely to do much.
So, from that tome I see most of the calcium in milk is in the form of calcium hydroxyphosphate. A drop in pH caused by acidifying bacteria converts some of this calcium into free calcium which forms stong bonds within the milk "particles" causing them to aggregate and expand until the milk coagulates.
Adding additional free calcium in the form of calcium chloride presumably accelerates this process.
Additionally the action of Rennet is extremely sensitive to free calcium concentration, with increased free calcium accelerating the second phase of Rennet action, coagulation and syneresis (curd formation to us!)
Dave