That statement grabs a file called content-post-format.php in the theme directory, depending on the post format. Posts will grab content.php since there is no post format.
Copy the information out of content.php into single-campsite.php and go from there. Alternatively, you can create a copy of content.php called content-campsite.php and call:
<?php get_template_part( 'content', 'campsite' ); ?>