Adavnced custom fields relationship query plus query inside

Looks like you’re using both get_posts() and new WP_Query() — You only need one or the other. You’re also using WP_Query() incorrectly — It’s looking for an array of arguments, but you’re passing $videos, which is an array of post objects.

Try this:

<?php

$args = array(
  'post_type' => 'videos',
  'meta_query' => array(
    'relation' => 'AND',
    array(
     'key' => 'speaker',
     'value' => get_the_ID()
    ),
    array(
     'key' => 'events',
     'value' => $eventid
    )
  )
);

$videos = new WP_Query($args);

if($videos->have_posts()) : 
   while($videos->have_posts()) : 
      $videos->the_post();

?>

<!-- STUFF FOR EACH VIDEO HERE -->
<a href="https://wordpress.stackexchange.com/questions/121699/<?php the_permalink(); ?>" ?>"><?php the_title(); ?></a>

<?php

endwhile;
endif;

?>

Untested. Hope it works for you.