Hi Serge,
The forum was down when I tried to answer.
You just have to investigate the properties of the objects you are dealing with:
http://adndevblog.typepad.com/manufacturing/2013/10/discover-object-model.html
E.g. in this case check the PartsListRow object: it has a Visible property which I think is exactly for that.
See modified code with the difference highlighted in red:
Sub ExportPartsListContent()
Dim oExcel As Object
Set oExcel = CreateObject("Excel.Application")
' For debugging
'oExcel.Visible = True
Dim oWB As Object
Set oWB = oExcel.Workbooks.Open("C:\temp\test.xlsm")
Dim oWS As Object
Set oWS = oWB.ActiveSheet
Dim oDoc As DrawingDocument
Set oDoc = ThisApplication.ActiveDocument
Dim oSheet As Sheet
Set oSheet = oDoc.ActiveSheet
' Export the first PartsList
Dim oPL As PartsList
Set oPL = oSheet.PartsLists(1)
' Starting cell position on the Excel sheet
Dim iRowStart As Integer: iRowStart = 1
Dim iColStart As Integer: iColStart = 1
' Export headers
Dim iRow As Integer: iRow = iRowStart
Dim iCol As Integer: iCol = iColStart
Dim oCol As PartsListColumn
For Each oCol In oPL.PartsListColumns
oWS.Cells(iRow, iCol).Value = oCol.Title
iCol = iCol + 1
Next
iRow = iRow + 1
' Export content
Dim oRow As PartsListRow
For Each oRow In oPL.PartsListRows
If oRow.Visible Then
iCol = iColStart
Dim oCell As PartsListCell
For Each oCell In oRow
oWS.Cells(iRow, iCol).Value = oCell.Value
iCol = iCol + 1
Next
iRow = iRow + 1
End If
Next
' Save it
' We disable the confirmation dialog
' in case the file already exists and
' needs to be overwritten
oExcel.DisplayAlerts = False
Call oWB.SaveAs("C:\temp\test2.xlsm")
' Close excel
Call oExcel.Quit
End Sub
Cheers,

Adam Nagy
Autodesk Platform Services