that code you found is part of the OOP class used by Easy Digital Downloads. Their docs are here: https://docs.easydigitaldownloads.com/article/1160-recurring-payments-developer-eddrecurringsubscriber
What you'd need to do is something like:
$my_user = get_current_user_id(); //grab current user
$subscriber = new EDD_Recurring_Subscriber( $my_user, true ); //pass user id to EDD class
//The EDD class will return its own user object, and on that you can do your check from the question:
if ($subscriber->has_active_subscription()) {
echo 'some special message for users with subscriptions';
} else {
//do something else
}
Watch out though, because that method will return true both if user has an active subscription and if he/she has a cancelled subscription (but false if subscription has expired). That may or may not be what you want.
I don't have EDD so haven't tested this but I hope it at least gets you started.