class example {
    public function __construct() {
        // option1: place here will work
        remove_action( 'woocommerce_before_shop_loop_item_title', 'woocommerce_template_loop_product_thumbnail', 10 );

        // wrong demonstration: will not work because original call is not a class, it is not necessary to use class method to remove
        // remove_action( 'woocommerce_before_shop_loop_item_title', array( $this 'woocommerce_template_loop_product_thumbnail' ), 10 );

        add_action( 'init', array( $this, 'init' ) );
    }

    // option2: if you want to ***group different actions*** together, it also works.
    public function init() {
        // place here also work
        // remove_action( 'woocommerce_before_shop_loop_item_title', 'woocommerce_template_loop_product_thumbnail', 10 );

        // other remove actions or actions
    } 
}

new example();

// your ' show_video' is already doing the job `show_video_if_set_else_image`
// so you might want to change this function name too
remove_action( 'woocommerce_before_shop_loop_item_title', 'woocommerce_template_loop_product_thumbnail', 10 );
add_action('woocommerce_before_shop_loop_item_title', array($this, 'show_video' ) );

    function show_video(){
        $linkk = get_post_meta(get_the_ID(), 'YT_video_link', true);
        $linkk = substr($linkk, -11);
        if($linkk != ''){
            echo 'show video';
            // if you put remove_action, it will not work as expected because the remove_action is run after add_action, so before it removes, it run already.

            ?>

remove_action( 'woocommerce_before_shop_loop_item_title', 'woocommerce_template_loop_product_thumbnail', 10 );