Comparação de dados de com null sempre dar false

static void printNodesOneChild(Node root){
  return;

 // resto do código, tornado irrelevante

static void printNodesOneChild(Node root)
{
    root = null; // muda root pra null, daí já não passa do primeiro if
    // Base case
    if (root == null)
        return;

Esse é o código completo, o print está sendo realizado na classe principal…

/*

* A binary tree node has data, pointer to left child and a pointer to right

* child

*/

public static class Node {

int data;

Node left, right;

Node(int data) {
        this.data = data;
    }
}


// static variable to point to the
// starting index of the string.
static int start = 1;

// Construct Tree Function which accepts
// a string and return root of the tree;
static Node constructTree(String s) {

	// Check for null or empty string
	// and return null;
	if (s.length() == 0 || s == null) {
		return null;
	}

	if (start >= s.length())
		return null;

	// Boolean variable to check
	// for negative numbers
	boolean neg = false;

	// Condition to check for negative number
	if (s.charAt(start) == '-') {
		neg = true;
		start++;
	}

	// This loop basically construct the
	// number from the continuous digits
	int num = 0;
	while (start < s.length() && Character.isDigit(s.charAt(start))) {
		int digit = Character.getNumericValue(s.charAt(start));
		num = num * 10 + digit;
		start++;
	}

	// If string contains - minus sign
	// then append - to the number;
	if (neg)
		num = -num;

	// Create the node object i.e. root of
	// the tree with data = num;
	Node node = new Node(num);

	if (start >= s.length()) {
		return node;
	}

	// Check for open bracket and add the
	// data to the left subtree recursively
	if (start < s.length() && s.charAt(start) == '(') {
		start++;
		node.left = constructTree(s);
	}

	if (start < s.length() && s.charAt(start) == ')') {
		start++;
		return node;
	}

	// Check for open bracket and add the data
	// to the right subtree recursively
	if (start < s.length() && s.charAt(start) == '(') {
		start++;
		node.right = constructTree(s);
	}

	if (start < s.length() && s.charAt(start) == ')') {
		start++;
		return node;
	}
	return node;
}



static Vector<Integer> list = new Vector<>();
 
// Function to find the nodes 
// having single child 
public static void printNodesOneChild(Node root)
{
    // Base case
    if (root == null)
        return;	  
    // Condition to check if the node
    // is having only one child
     System.out.println(root.right.data );
    if (root.left !=  null && root.right == null ||
        root.left == null && root.right != null)
    {
        list.add(root.data);
    }
     
    // Traversing the left child
     printNodesOneChild(root.left);
     
    // Traversing the right child
    printNodesOneChild(root.right);
}



// Driver Code
public static void main(String[] args) {
	Scanner input = new Scanner(System.in);
	// Input
	String s = "(33(9(0(1()())())(2(3()())(4()())))(11(5()(6()()))(8(7()())())))";
    //String s = "(7(11(9()())(2()()))(13(0()())(1()())))";

	// Call the function cunstruct tree
	// to create the tree pass the string;
	Node root = constructTree(s);

	// Function to print preorder of the tree
	printTree(root);

	    printNodesOneChild(root);
	 
	    // Condition to check if there is
	    // no such node having single child
	    System.out.println(list.size());
	    if (list.size() == 0)
	        System.out.println(-1);
	    else
	    {
	        for(int value : list)
	        {
	            System.out.println(value);
	        }
	    }
	 
	}

	System.out.println();		

}

public static void printNodesOneChild(Node root)
{
    // Base case
    if (root == null)
        return;	  
    // Condition to check if the node
    // is having only one child
     System.out.println(root.data); // alterado de root.right.data
    if (root.left !=  null && root.right == null ||
        root.left == null && root.right != null)
    {
        list.add(root.data);
    }
     
    // Traversing the left child
     printNodesOneChild(root.left);
     
    // Traversing the right child
    printNodesOneChild(root.right);
}