As you are targeting a specific email notification, first we need to get the Email ID to target the "New Order" email notification. The only way is to get it before and to set the value in a global variable.

Then in a custom function hooked in woocommerce_order_item_meta_end action hook, we display the product description exclusively for New Order email notification.

Here is that code:

 ## Tested on WooCommerce 2.6.x and 3.0+

// Setting the email_is as a global variable
add_action('woocommerce_email_before_order_table', 'the_email_id_as_a_global', 1, 4);
function the_email_id_as_a_global($order, $sent_to_admin, $plain_text, $email ){
    $GLOBALS['email_id_str'] = $email->id;
}

// Displaying product description in new email notifications
add_action( 'woocommerce_order_item_meta_end', 'product_description_in_new_email_notification', 10, 4 );
function product_description_in_new_email_notification( $item_id, $item, $order = null, $plain_text = false ){

    // Getting the email ID global variable
    $refNameGlobalsVar = $GLOBALS;
    $email_id = $refNameGlobalsVar['email_id_str'];

    // If empty email ID we exit
    if(empty($email_id)) return;

    // Only for "New Order email notification"
    if ( 'new_order' == $email_id ) {

        if( version_compare( WC_VERSION, '3.0', '<' ) ) { 
            $product_id = $item['product_id']; // Get The product ID (for simple products)
            $product = wc_get_product($item['product_id']); 
        } else {
            $product = $item->get_product();
            
            if( $product->is_type('variation') ) {
                $product = wc_get_product( $item->get_product_id() );
            }
        }

        // Get the Product description (WC version compatibility)
        if ( method_exists( $item['product'], 'get_description' ) ) {
            $product_description = $product->get_description(); // for WC 3.0+ (new)
        } else {
            $product_description = $product->post->post_content; // for WC 2.6.x or older
        }

        // Display the product description
        echo '<div class="product-description"><p>' . $product_description . '</p></div>';
    }
}

This code goes in function.php file of your active child theme (or theme) or also in any plugin file.

This code is tested and works.

Code Update and Error explanations in woocommerce_order_item_meta_end action hook:

PHP Warning for woocommerce_order_item_meta_end (Mike Joley)