Can checkboxes be set to "checked" when using wp_set_object_terms?

I'm using PHP to pull values from arrays in an API and add them to custom taxonomy within custom post types in Wordpress.

          $game_tags = array(
                 $games['tags'][0]['name'],
                 $games['tags'][1]['name'],
                 $games['tags'][2]['name'],
             );

        $term_taxonomy_ids = wp_set_object_terms( $games_slug, $game_tags, 'tags_list', true );

All works okay, and the custom taxonomy tags_list is populated with the values of $game_tags, but all values are unchecked.

Is there a way to automatically check all values while or after they are added?