"SyntaxError: Unexpected token ' in JSON at position 0" when requiring a module using strict mode

In index.js I have

'use strict';

const config = require('./config');

In config.js I have

'use strict';

const config = new function() {
  this.port = 3000;
  this.redirectUri = "http://localhost:" + this.port + "/auth";
}

module.exports = config;

On x64 Windows running node v6.9.5 this runs fine.

On a Raspberry Pi Zero (Raspbian Pixel, ARM v6) running node 6.10.2 however, I get the following error:

module.js:590
    throw err;
    ^

SyntaxError: /home/pi/pihas-api/config.json: Unexpected token ' in JSON at position 0
    at Object.parse (native)
    at Object.Module._extensions..json (module.js:587:27)
    at Module.load (module.js:487:32)
    at tryModuleLoad (module.js:446:12)
    at Function.Module._load (module.js:438:3)
    at Module.require (module.js:497:17)
    at require (internal/module.js:20:19)
    at Object.<anonymous> (/home/pi/pihas-api/index.js:8:16)
    at Module._compile (module.js:570:32)
    at Object.Module._extensions..js (module.js:579:10)

I know this is because I'm using 'use strict'; in config.js, but I'm wondering why it does work on Windows, and whether or not there's a way to get this to work on the Pi Zero as well.

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