Source code for https://victorfont.com/filter-wordpress-query-by-post-format/

filter_video_format_posts.php

<?php

function filter_video_format_posts($query) {
    /* change 999 to the page id for your archive page */
    if ( !is_page ('999') )
        return $query;

    $taxquery = array(
        array(
            'taxonomy' => 'post_format',
            'field'    => 'slug',
            'terms'    => array( 'post-format-video' ),
        )
    );
    $query->set( 'tax_query', $taxquery );
}
add_action( 'pre_get_posts', 'filter_video_format_posts' );