Sort custom post type by custom datepicker instead of filtering

In meta_query, you missed the type of the field:

$args = array( 
'post_type' => 'events',
'posts_per_page' => '-1',
'meta_query' => array(
    array(
        'key' => 'event_date_start' ,
        'compare' => '>=',
        'value' => current_time('Ymd'),
        'type' => 'DATE',
    )
),
'meta_key' => 'event_date_start',
'orderby' => 'meta_value_num',
'order' => 'ASC'

);