Проверь это...
Я протестировал. Валидация работает.
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Test HTML5 with Date Picker</title>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.css">
<script src="https://code.jquery.com/jquery-1.12.4.js"></script>
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.js"></script>
<script>
$( function() {
$( "#datepicker" ).datepicker();
} );
</script>
</head>
<body>
<form action="#" method="post">
<p>Name: <input type="text" id="name" required></p>
<p>Date: <input type="text" id="datepicker" required></p>
<input type="submit" value="Submit" />
</form>
</body>
</html>