Check if meta key value already exists

Just do a query with WP_Query using the Custom Field parameters (meta_query) to look for posts with the meta key and the value – exemplary code:

 // args to query for your key
 $args = array(
   'post_type' => 'your_post_type',
   'meta_query' => array(
       array(
           'key' => 'videoid',
           'value' => $new_posts_videoid  // for example: '111'
       )
   ),
   'fields' => 'ids'
 );
 // perform the query
 $vid_query = new WP_Query( $args );

 $vid_ids = $vid_query->posts;

 // do something if the meta-key-value-pair exists in another post
 if ( ! empty( $vid_ids ) ) {
     // do your stuff
 }

There is no need to use query_post() – see:
When should you use WP_Query vs query_posts() vs get_posts()?
. If you need a complete array of post objects, not just the ids, remove 'fields' => 'ids'.