VBA Error 13 Type Mismatch

You have a couple of issues there. First, if you use the Text property of a multiple cell range, it will return Null unless all the cells contain the same text. Second, as you note, you cannot add an array in one go using AddItem - you need to add an item then loop to populate the columns, remembering that the indices are 0-based:

With TabData.DataTable
   .AddItem
   For n = 1 to LastColRA
      .List(.ListCount - 1, n - 1) = Sheet1.Cells(x + 2, n).Value
   next n
End With

Here's a version that will work with more than 10 columns:

Dim i As Long, counter As Long, counter_RA As Long, x As Long
Dim LastColRA As Long, LastColCP As Long
Dim vList()


LastColRA = Sheet1.Cells(1, Columns.Count).End(xlToLeft).Column
LastColCP = Sheet2.Cells(1, Columns.Count).End(xlToLeft).Column


'Check to make sure that enough items were selected
For x = 0 To ListBox2.ListCount - 1
    If ListBox2.Selected(x) Then
        counter_RA = counter_RA + 1
        ReDim Preserve vList(1 To LastColRA, 1 To counter_RA)
        For i = 1 To LastColRA
            vList(i, counter_RA) = Sheet1.Cells(x + 2, i).Value
        Next i
    End If
Next x
For x = 0 To ListBox1.ListCount - 1
    If ListBox1.Selected(x) Then
        counter_RA = counter_RA + 1
        ReDim Preserve vList(1 To LastColRA, 1 To counter_RA)
        For i = 1 To LastColRA
            vList(i, counter_RA) = Sheet2.Cells(x + 2, i).Value
        Next i
    End If
Next x

With TabData.DataTable
    .ColumnCount = LastColRA
    .Column = vList
End With