I didn't succeed in building Greenworks myself last time, but two new pre-built versions of Greenworks have become available: one for NW.js 0.14.7 (the LTS branch) using Steamworks SDK 1.37, although for some reason this one omits the 32-bit platforms, and one for NW.js 0.15.0 (the second-newest) using Steamworks SDK 1.36, which includes all the platforms. I tested both and they both worked for me, so I've updated the original post in this thread with the new versions.
I also revised the instructions on how to get it working to be clearer. It's also important to make sure you match the right NW.js version and Steamworks SDK version for the Greenworks version you are using. If any versions are different it seems to cause compatibility problems. We didn't have a NW.js-for-C2 build for 0.14.7, so I added it to make sure you can match the versions exactly.
I don't know why the 0.14.7 release omits Greenworks for 32-bit Windows and Linux, but the 0.15 version has them all, so that looks like the best candidate for the time being. I don't know why the Greenworks team don't publish more releases, and I don't know why my own builds never seem to work (I may look in to that again if it's a long time before the next update), but hopefully at some point support for NW.js 0.16+ will appear too. NW.js 0.15 is based on Chrome 51 so that's a reasonably modern version to work with for the time being.
Since it's a bit messy trying to match an exact NW.js version and Steamworks SDK version, I don't think we can realistically ship the Greenworks plugin as built-in to C2. Since NW.js can update independently of C2, having a fixed Greenworks plugin version built-in to C2 would break easily. Assuming the latest releases work OK, I think it would be better to add another table to the scirra.com/nwjs page listing all the Greenworks plugin releases available and the NW.js & Steamworks SDK versions they use, and then you can download whichever you want to work with, instead of being stuck with some fixed built-in version. So I think that would be the best we can do for officially providing the plugin.
Let me know how everything works out.