In case anyone is interested, I solved the problem. Here's how:
1. I ran eclipse from Cygwin: <path_to_eclipse_folder>/eclipse.exe & (maybe I should have done this from the beginning, but I followed the tutorial where it said nothing about Cygwin)
2. In eclipse, right click on project folder -> Properties -> C++ Build -> Builder Settings tab -> Build command: bash <path_to_android_NDK_folder>\android-ndk-r8\ndk-build
3. Click Apply, and the project is rebuilt with no errors.
Done :)