The problem is that you are replacing each selection with the next what you need is

Public Sub cmdOK_Click()
Dim intListBox As Integer
Dim strText As String

    For intListBox = 0 To ListBox1.ListCount - 1
        If ListBox1.Selected(intListBox) Then
            If strText = "" Then
                strText = ListBox1.List(intListBox)
            Else
                strText = strText & Chr(11) & ListBox1.List(intListBox)
            End If
        End If
    Next intListBox
    ActiveDocument.FormFields("Hinweise").Result = strText
    Hide
lbl_Exit:
    Exit Sub
End Sub