SyntaxError: 'import' and 'export' may appear only with 'sourceType: module' - Gulp

Consider the following two files:

app.js

import Game       from './game/game';
import React      from 'react';
import ReactDOM   from 'react-dom';

export default (absPath) => {
  let gameElement = document.getElementById("container");

  if (gameElement !== null) {
      ReactDOM.render(
          <Game mainPath={absPath} />,
          gameElement
      );
  }
}

index.js

import App from './src/app';

The gulpfile.js

var gulp        = require('gulp');
var source      = require('vinyl-source-stream');
var browserify  = require('browserify');
var babelify    = require("babelify");
var watch       = require('gulp-watch');

gulp.task('make:game', function(){
  return browserify({
    entries: [
      'index.js'
    ]
  })
  .transform('babelify')
  .bundle()
  .pipe(source('index.js'))
  .pipe(gulp.dest('app/'));
});

The error:

gulp make:game
[13:09:48] Using gulpfile ~/Documents/ice-cream/gulpfile.js
[13:09:48] Starting 'make:game'...

events.js:154
      throw er; // Unhandled 'error' event
      ^
SyntaxError: 'import' and 'export' may appear only with 'sourceType: module'

What is this error? What am I doing wrong?

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