All results that I came across when performing a search for export listview to excel were related to instances of Windows.Forms.ListView and not System.Web.UI.WebControls.ListView.

Attached are the two functions necessary to export instances of System.Web.UI.WebControls.ListView to Excel.

public override void VerifyRenderingInServerForm(Control control) { }

protected void btnExport_Click(object sender, EventArgs e)
{
    Response.Clear();
    Response.Buffer = true;
    Response.ContentType = "application/vnd.ms-excel";
    Response.Charset = "";
    this.EnableViewState = false;
    StringWriter stringWriter = new StringWriter();
    HtmlTextWriter htmlTextWriter = new HtmlTextWriter(stringWriter);
    listView.RenderControl(htmlTextWriter);
    Response.Write(stringWriter.ToString());
    Response.End();
}