How to display only one category in a custom post type?

Something like this should work but you haven’t stated where you want to display the CPT pages for games.

function display_games_archive( $query ) {

if ( !is_admin() || $query->is_main_query() && is_post_type_archive( 'portcat' ) ) {

    $query->set( 'category__in', 'games' );
    return;
    }
}
add_action( 'pre_get_posts', 'display_games_archive', 1 );