No you don’t remove it from /wp-includes/post-template.php. This is a WordPress core file and you should never edit any WordPress core file.

The answer is talking about removing the call of wp_link_pages function within a template file.

Which template file to edit depends on the theme and the URL you are visiting. Typically it should be /wp-content/themes/<your-active-theme>/single.php.

But templates can be divided in multiple files and call to wp_link_pages function may be in any of those template part files.

For example, in twentyseventeen theme, it can be found on multiple files. For pages, it’s in:

/wp-content/themes/twentyseventeen/template-parts/page/content-page.php:

For posts, it’s in:

/wp-content/themes/twentyseventeen/template-parts/post/content-audio.php
/wp-content/themes/twentyseventeen/template-parts/post/content-gallery.php
/wp-content/themes/twentyseventeen/template-parts/post/content-image.php
/wp-content/themes/twentyseventeen/template-parts/post/content-video.php
/wp-content/themes/twentyseventeen/template-parts/post/content.php

If you still cannot find which template file to edit for your currently active theme, you may read this guide to find out.

Read more about WordPress theme template files for posts and pages.

Also, while you remove the wp_link_pages function call from any template file, make sure you have basic understanding of PHP function calls. Since the function call may involve multiple lines.

Update: How to remove wp_link_pages pagination from a Genesis Theme:

(Since it’s mentioned in the comment that it’s the Genesis LifeStyle Pro Theme)

Themes with Genesis framework handle pagination differently. With a Genesis Theme, you’ll not actually find an explicit call to the wp_link_pages pagination function in the template files, as it’s handled by the Genesis framework.

So in that case, remove the the CODE you used in the question, and instead, use the following CODE:

add_filter( 'the_content', function( $content ) {
    remove_action( 'genesis_entry_content', 'genesis_do_post_content_nav', 12 );
    return $content . wp_link_pages( array( 'echo' => FALSE ) );
}, -1 );

Now you’ll not have the default pagination provided by your Genesis theme.