Use gulp to select and move directories and their files

You need to include the base option to src, which will preserve the file structure the way you want:

var filesToMove = [
        './_locales/**/*.*',
        './icons/**/*.*',
        './src/page_action/**/*.*',
        './manifest.json'
    ];

gulp.task('move',['clean'], function(){
  // the base option sets the relative root for the set of files,
  // preserving the folder structure
  gulp.src(filesToMove, { base: './' })
  .pipe(gulp.dest('dist'));
});

Also, you are probably going to have trouble down the road if you have all these source files in the root of your project.

If you can, I’d recommend you use a single src/ folder and move all your application-specific files into there. This makes maintenance easier moving forward, and prevents your build-specific files from getting mixed up with your application-specific files.

If you do this, then simply replace all occurrences of ./ with src/ in the example above.