Why the decorator pattern implementation requires a common abstract super-class with the core class?

I'm experimenting with the decorator design pattern in c++. However, I was not able to implement it without an abstract super-class from which both the core and decorating classes inherit.

I don't understand why abstract super-class is needed.

My working decorator example:

#include <string>
#include <iostream>
using namespace std;

// abstract superclass
class Pizza
{
  public:
    virtual string GetDescription() = 0;
    virtual int GetCost() = 0;
};

// base class that can be extended
class Margharita: public Pizza 
{ 
   private:
    string description;
    int cost;
   public:
     Margharita(string t, int c){description = t; cost = c;} 
     string GetDescription(){return(description);}
     int GetCost(){return(cost);}
}; 

// decorator class that extends base class
class ExtraCheese: public Pizza
{
   private:
    Pizza* pizza;

   public:
    // constructor
    ExtraCheese(Pizza* p) {pizza = p;}

    string GetDescription() { return (pizza->GetDescription() + ", Extra Cheese"); } 
    int GetCost() {  return(pizza->GetCost() + 20); } 
};

int main()
{
  // create decorated object
  Pizza* pizza = new ExtraCheese(new Margharita("Margharita", 100));
  cout <<  pizza->GetDescription() << '\n';
  cout << pizza->GetCost() << '\n';
}

that gives the output: Margharita, Extra Cheese 120.

If I remove the abstract super-class, the decoration stops working:

#include <string>
#include <iostream>
using namespace std;

// base class that can be extended
class Pizza
{
  private:
   string description;
   int cost;
  public:
    Pizza(){description = "Pizza"; cost = 100;};
    string GetDescription(){return(description);}
    int GetCost(){return(cost);}
}; 

// decorator class that extends base class
class ExtraCheese: public Pizza
{
   private:
    Pizza* pizza;

   public:
    // constructor
    ExtraCheese(Pizza* p) {pizza = p;}

    string GetDescription() { return (pizza->GetDescription() + ", Extra Cheese"); } 
    int GetCost() {  return(pizza->GetCost() + 20); } 
};

int main()
{
  // create decorated object
  Pizza* pizza = new ExtraCheese(new Pizza());
  cout <<  pizza->GetDescription() << '\n';
  cout << pizza->GetCost() << '\n';
}

In this case the output only shows the attributes of the core object (Pizza 100).

Why is this happening?