See on how SQLDataAdapter is used with command as parameter: MSDN: SqlDataAdapter Constructor (SqlCommand)
Internally, it's the Select command that is initialized for it.
Try to use it like this as it will be simple to read and understand:
con = new SqlConnection(connection);
SqlCommand command = new SqlCommand("[dbo].[StoredProc1]", con);
command = new SqlCommand(qry, con);
command.Parameters.Add("@player_id", SqlDbType.NVarChar).Value = DropDownList1.SelectedValue;
command.CommandType = CommandType.StoredProcedure;
SqlDataAdapter da = new SqlDataAdapter();
da.SelectCommand = command;
Further, you need to bind the list with a datatable and not dataset.
ListBox1.DataSource = ds.Tables;
ListBox1.DataTextField = "player_id";