What are the minimum requirements to charge the 2016 MacBook Pros?
After some experimentation with a 2016 15" MBP, it seems that they are very flexible:

A USB charger capable of 5 V, 2.4 A proprietary Apple signalling was recognized as providing 12 W of power, and an iPhone charger (which complies the USB BC specification) was shown as providing 5 W. The Nexus 5X charger, which provides USB-C 5 V, 3 A charging, was also correctly recognized as providing 15 W.

The power settings were showing these as "not charging" with the Mac running, but it turns out that even the large 15" MBP is capable of slowly charging from the tiny 5 V, 1 A adapter (it went up by about 2% after charging in sleep mode for about half an hour).