Your sample documents do not reflect the details you provided so it is no wonder it did not work. Based on your revised example the following will work and will also allow for the spelling error.
Code:
Sub CopyNamesToExcel()
Dim oTable As Table
Dim oRng As Range
Dim xlApp As Object
Dim xlBook As Object
Dim xlSheet As Object
Dim xlCell As Object
Dim i As Integer, j As Integer
Dim sName As String
On Error Resume Next
Set xlApp = GetObject(, "Excel.Application")
If Err Then
Set xlApp = CreateObject("Excel.Application")
End If
On Error GoTo 0
Set xlBook = xlApp.Workbooks.Add
Set xlSheet = xlBook.Sheets(1)
xlApp.Visible = True
'Set xlCell = xlSheet.Range("A1")
'xlCell.value = "Name"
'j = 2
j = 1
For Each oTable In ActiveDocument.Tables
Set oRng = oTable.Cell(1, 2).Range
oRng.End = oRng.End - 1
If InStr(1, oRng.Text, "NAMES OF PERSON") > 0 Then
sName = Replace(oRng.Text, "NAMES OF PERSON", "")
sName = Replace(sName, "VOLUNTARIY RETIRED", "") '? Spelling
sName = Replace(sName, "VOLUNTARILY RETIRED", "")
sName = Replace(sName, Chr(13), "")
Set xlCell = xlSheet.Range("A" & j)
xlCell.value = Trim(sName)
j = j + 1
End If
Next oTable
End Sub