get a single latest post.

Use a WP_Query for each link.

Something like:

<?php
$video_query_args = array( 'category_name' => 'videos', 'posts_per_page' => 1 );
$video_query = new WP_Query( $video_query_args );

if ( $video_query->have_posts() ) :
    while ( $video_query->have_posts() ) : $video_query->the_post();
?>
<span class="homeblueTitle"><a href="<?php the_permalink(); ?>">video</a></span>
<?php
    endwhile;
endif;
wp_reset_postdata();
?>