How can I get next/ previous post links to order by a filter (by the last word of the title)?

Reviewing the MySQL string functions, it looks like you could use the SUBSTRING_INDEX() function:

ORDER BY SUBSTRING_INDEX( p.post_title, ' ', -1 ) {ASC|DESC} LIMIT 1

to order by the last word of the post title.

You could test this method within your orderby filters.

Example: Prev/Next CPT – ordered by last word in post title

This is an example how one could try to modify the linked answer by @WillLanni:

a) Next part for the custom post type cpt:

// Next CPT
add_filter( 'get_next_post_where', function( $where, $in_same_term, $excluded_terms )
{
    global $post, $wpdb;

    // Edit this custom post type to your needs
    $cpt="post";

    // Current post type
    $post_type = get_post_type( $post );

    // Nothing to do    
    if( $in_same_term || ! empty( $excluded_terms ) || $cpt !== $post_type )
        return $where;

    // Next CPT order by last word in title
    add_filter( 'get_next_post_sort', function( $orderby ) 
    {
        return " ORDER BY SUBSTRING_INDEX( p.post_title, ' ', -1 ) ASC LIMIT 1 ";
    } );

    // Modify Next WHERE part
    return $wpdb->prepare( 
        " WHERE 
            SUBSTRING_INDEX( p.post_title, ' ', -1 ) > SUBSTRING_INDEX( '%s', ' ', -1 ) 
            AND p.post_type="%s" 
            AND p.post_status="publish"
        ", 
        $post->post_title, 
        $post_type 
    );    

}, 10, 3 );

b) Previous part for the custom post type cpt:

// Previous CPT
add_filter( 'get_previous_post_where', function( $where, $in_same_term, $excluded_terms)
{
    global $post, $wpdb;

    // Edit this custom post type to your needs
    $cpt="post";

    // Current post type
    $post_type = get_post_type( $post );

    // Nothing to do    
    if( $in_same_term || ! empty( $excluded_terms ) || $cpt !== $post_type )
        return $where;

    // Previous CPT, order by last word in post title
    add_filter( 'get_previous_post_sort', function( $orderby )
    {
        return " ORDER BY SUBSTRING_INDEX( p.post_title, ' ', -1 ) DESC LIMIT 1 ";
    } );

    // Modify Prev WHERE part
    return $wpdb->prepare( 
        " WHERE 
            SUBSTRING_INDEX( p.post_title, ' ', -1 ) < SUBSTRING_INDEX( '%s', ' ', -1 ) 
            AND p.post_type="%s" 
            AND p.post_status="publish"
        ", 
        $post->post_title, 
        $post_type 
    );

}, 10, 3 );

where you modify the custom post type 'cpt' to your needs.