Please try this way:
Change date, the_date, the_time to get_date, get_the_date, get_the_time.
function KhmerNumDate ($text) {
$text = str_replace('1', '១', $text);
$text = str_replace('2', '២', $text);
$text = str_replace('3', '៣', $text);
$text = str_replace('4', '៤', $text);
$text = str_replace('5', '៥', $text);
$text = str_replace('6', '៦', $text);
$text = str_replace('7', '៧', $text);
$text = str_replace('8', '៨', $text);
$text = str_replace('9', '៩', $text);
$text = str_replace('0', '០', $text);
return $text;
}
add_filter('get_date', 'KhmerNumDate');
add_filter('get_the_date', 'KhmerNumDate');
add_filter('get_the_time', 'KhmerNumDate');