No, this is
classic load ([gallery] shortcode).
Gallery page from the demo website uses attached images from Media Manager, there's no need to write any links or shortcodes to images gallery1.jpg, gallery2.jpg in your page editor.
Only upload e.g. new image, then in Media Library ("Uploaded to" column) click "Attach" button, and choose your page (eg. page_id =121 - Gallery page, see an attachment).