Thanks for the link. After reading a bit about H1B1 it looks like
1. It is included in the H1B cap, ergo it is de facto capped
2. It is actually capped as a portion of the available H1B.
"Of the 65,000 visas allocated to the capped H-1B visa program, the amount of 6,800 are reserved for use for the H-1B1: 1,400 for Chile and 5,400 for Singapore."
Counted separately but included in the overall cap.
Another interesting difference is that H1B1 seems to not be dual intent, contrary to H1B. Definitely not the panacea that was hinted at in this thread.
No clue what parent meant by virtually uncapped.