There many strange solutions on it. It seems that the authors simply did not understand how and when the shortcode [embed] works. Here is the simple code which can be added to functions.php.
/**
* Allows to show video in excerpt.
*
* @param string $post_excerpt
*
* @return string
*/
function get_the_excerpt_filter( $post_excerpt ) {
$pos = mb_strpos( $post_excerpt, '' );
if ( false !== $pos ) {
/** @var WP_Embed $wp_embed */
$wp_embed = $GLOBALS['wp_embed'];
$post_excerpt = $wp_embed->run_shortcode( $post_excerpt );
}
return $post_excerpt;
}
add_filter( 'get_the_excerpt', 'get_the_excerpt_filter' );
The code properly process the shortcode like [embed]https://www.youtube.com/watch?v=ouiHvUCI_pw[/embed] in post excerpt and shows the video.