Hi Kyle,
I happen to be the one who is maintaining that GNOME Live! page, thanks for letting me know this situation.
Please note that at this moment as there are significant stability and functionality issues with Cairo 1.12.x on Windows, probably the best bet is to use 1.10.2 for now-so I will update the notes on that page about this as well (as you probably have noticed, the instructions there applied to 1.10.x :))
If someone knows the updated situation about Cairo 1.12.x+ on Windows, it would be really appreciated on my side at least.
With blessings,
Chun-Wei Fan
Unfortunately, I don't think they apply to the latest build of Cairo (as of writing, 1.12.2).