I certainly can’t argue with you on that one. I’ll be interested to hear how they respond to you on this - based on the OP’s question is definitely seems like the text would benefit from the addition of a simple explanatory paragraph.
They said that the one formula was for computing the number of (futures) contracts, while the other was for computing the notional value (of a swap).
I agreed, but stressed that that didn’t really explain the difference in divisors, as they’re both computing basis point values. I asked for clarification, and mentioned that the question had already been asked here.
In real world, you would have picked an arbitrary notional for the swap (10, 100, 500, 1000, 10000), and compute the BPV based on that notional. And when you want to compute the BPV per $1 notional, just divide the computed BPV by the notional chosen