SelectedItems
is the key!
I prepared SampleData as described here and capture checked items with following code.
System.Collections.ObjectModel.ObservableCollection<object> selected_items = radTreeListView.SelectedItems;
foreach (object item in selected_items)
{
WarehouseItem warehouseitem = (WarehouseItem)item;
MessageBox.Show(warehouseitem.Name);
}