Let's draw a list

  IntListItem -> IntListItem -> IntListItem

and then draw the position of the list head:

  IntList -> IntListItem -> IntListItem -> IntListItem

You can see that the if-branch in the cs101 answer comes because there is a ('virtual') element of the list (the IntList head) that is different from the other elements of the list.

If we were to make them the same (C# code):

  interface IListItem 
  {
     IntListItem Next {get;set;}
  }

  class IntListItem : IListItem
  {
     int Value {get; set;}
     IntListItem Next {get; set;}
  }

  class IntList : IListItem
  {
     IntListItem Head {get; set;}
     IntListItem Next 
     {
        get { return Head; }
        set { Head = value; } 
     }
  }

then our cs101 code simplifies itself, folding into a prettier algorithm:

  void remove_cs102(IntList l, IntListItem target)
  {
     IListItem p = (IListItem) l;
     while (p.Next != target) 
     { 
        p = (IListItem) p.Next;
     }
 
     p.Next = p.Next.Next;
  }

the use of indirect pointers was masking the real issue: some algorithms look better if you add a virtual head (or a virtual tail) to your linked list. Emphasis on look though -- they work almost the same.