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?

Older versions of Babel came with everything out of the box. The newer version requires you install whichever plugins your setup needs. First, you'll need to install the ES2015 preset.

npm install babel-preset-es2015 --save-dev

Next, you need to tell babelify to use the preset you installed.

return browserify({ ... })
  .transform(babelify.configure({
    presets: ["es2015"]
  }))
  ...

Source