UPDATE & SOLVED - Found the problem. The source image I used to create the .icns file was 1024x1024. I resized the source to 512x512 and rebuilt my Electron app. The correct app appeared.
I know this sounds crazy, but the wrong icon is displayed in the OS X Dock when I run my app.
In Finder, my app has the wrong icon. Looks like a piece of paper with a ruler, pencil and brush.
However, if I view my app's "Package Contents", go the Resources folder, the atom.icns is my icon. I can open it using the Preview app.
Any idea why the atom.icns file in the Resources folder is not being used by OS X for the Finder app icon and the Dock icon?
Thank you,
Karl
Wow we had the same issue and was on rabbit chase until I found this! Our icon 1024x1024 was working on retina displays but would break on others. Thank you for posting this.
It seems your ICNS is invalid or your icns app maker is not good. My source icon is 1024 and it works on retina and non-retina iMac. Consider using http://www.img2icnsapp.com app.
Could you please send me or attach here your ICNS files? So I can check it and add validation? (I am electron-builder maintainer and I think that it will be cool if electron-packager will check such errors and report).
I think that it will be cool if electron-packager will check such errors and report
I would like to note that if electron-packager were to do that, I would prefer to see the icon checker code for that in a separate module (because that's certainly not an electron-packager specific function), and then we would integrate that module into the current icon code.
Just change extension from png to icns

Most helpful comment
It seems your ICNS is invalid or your icns app maker is not good. My source icon is 1024 and it works on retina and non-retina iMac. Consider using http://www.img2icnsapp.com app.
Could you please send me or attach here your ICNS files? So I can check it and add validation? (I am electron-builder maintainer and I think that it will be cool if electron-packager will check such errors and report).