You are looking at the HTML representation of the XML format.
HTML is good for debugging, but is unsuitable for application use.
Specify the format parameter to change the output format.
To see the non HTML representation of the XML format, set format=xml.
See the complete documentation, or API help for more information. 
<?xml version="1.0"?>
<api>
  <query-continue>
    <allredirects arcontinue="Irish_Dance_Wiki|1692" />
  </query-continue>
  <query>
    <allredirects>
      <r ns="0" title="Cass-Barrington Academy of Irish Dance" />
      <r ns="0" title="Ceili Dance" />
      <r ns="0" title="Cosa Meara Company of Irish Dance" />
      <r ns="0" title="Cosa Meara Company of Irish Dance" />
      <r ns="0" title="Cosa Meara Company of Irish Dance" />
      <r ns="0" title="DanceMinder" />
      <r ns="0" title="Dance Clothing" />
      <r ns="0" title="Dance Sean-Nós" />
      <r ns="0" title="Emerald School of Irish Dance" />
      <r ns="0" title="Instructional Videos" />
    </allredirects>
  </query>
</api>