I know - it's all a bit confusing at first, but you'll quickly pick things up I'm sure. I think you should be using Webstorage link to Webstorage in Manual rather than Node Webkit (maybe the word Web is confusing things here) if you're using a browser or wrapper on mobile. To keep things easy to read and understand in your event sheet, I suggest you first load the array into a string variable and then save that variable to Webstorage. Then, on game resume you do the reverse - load the Webstorage string into a variable and then load that into the array. You've already got the basics, looking at your event sheet, but the node webkit isn't going to work for you here.
Something like this:
On game end:
1. Set MyVariableString to MyGameArray.AsJSON
2. WebStorage: set local value ( Key: "SaveData" , Value: MyVariableString )
On game resume:
1. Set MyVariableString to WebStorage.LocalValue("SaveData")
2. MyGameArray : Load (MyVariableString)
In my limited experience I've had no problem using this technique to save data on android and ios using cocoonjs and phonegap (and, I think, Intel XDK as well - the old one, mind, not Crosswalk which I haven't tested extensively yet).
I hope this helps - let me know if it's not clear!