The XSLT mediator was created for SDL Tridion R5.3 up until 2011, since in SDL Tridion 2013, a new Template Building Block type was added, the XSLT template.
That was done by adding the XSLT mediator to the release basically, rendering the mentioned extension void. So you should NOT try to install the XSLT mediator extension, just use the built in one instead.
Not sure if the upgrade process will notice you already have the XSLT mediator extension installed and if it will correctly remove it, just check your
Tridion.ContentManager.config file and make sure you have the following Template Type (taken from my 2013 SP1 config):
<add id="10" name="XsltTemplate" titleResource="lblXsltTemplate" mimeType="text/xsl" hasBinaryContent="false" contentHandler="Tridion.ContentManager.Templating.Xslt.XsltTemplateContentHandler, Tridion.ContentManager.Templating, Version=220.127.116.110, Culture=neutral, PublicKeyToken=360aac4d3354074b">
<add itemType="TemplateBuildingBlock" fileExtension="xslt"/>
And make sure there are no additional template types mapped to the extension
xslt or mimetype
You will also want to remove the XSLT mediator extension DLLs from the bin folder and the GAC (if they were there).