You're fully wrong. The CoffeeScript compiler is written in CoffeeScript and you find it in the extras/coffee-script.js JavaScript file. If you can load that in some JS runtime environment, no need for Node/NPM.
Cygwin is the current way of "Node on Windows" but there will be much better / "more native" Node support for Windows coming in the next 4-20 months ;)) anyway, you don't need Node for Coffee. It only provides the Node integration pieces because the developer(s) do a lot of Node work themselves and it's a great way to write server-side code for Node for people coming from Python/Ruby etc.
Cygwin is the current way of "Node on Windows" but there will be much better / "more native" Node support for Windows coming in the next 4-20 months ;)) anyway, you don't need Node for Coffee. It only provides the Node integration pieces because the developer(s) do a lot of Node work themselves and it's a great way to write server-side code for Node for people coming from Python/Ruby etc.