I created this plugin that uses a shortcode to call wp_remote_get with parameters you pass to parsed and display a bit of HTML from a page on another site. You can include this shortcode in your page or post.
Here is an example of the shortcode that will display the Download Stats page for this Plugin on WordPress.org:
[remote_get url="https://wordpress.org/plugins/shortcurl/" start='<div class="entry-meta"' stop='!-- .entry-meta --' length="-1"].
and this is what you get: