Do you know what version of Outlook 2013 is installed? Your patch level supports 2013 32 bit, but doesn't officially support any of the SP levels that may exist or the 64 bit version.
The add-ins are version specific, so the ALM 11.5x add-in will not work for the ALM 11 version of software. I would download the ALM 11 specific version, then uninstall all of the prior versions of the add-in that may have been installed, and then run the ALM client registration and connectivity add-ins (they are necessary to register the client allowing the usage of third party add-ins like the Word and Excel add-ins yes they have released versions that state no admin privileges needed, as for the most part those extra rights are needed to run the registration and connectivity add-ins, as registering insures that obstacle is avoided, and then try and install the add-in again.
Here is a link to the latest supported environments for the various versions (server and client side) for your future reference: http://admhelp.microfocus.com/alm/specs/alm-qc-system-requirements.htm
As for 64 bit versions of Office (and this is support for the Excel add-in only, as no other 64 bit office applications are supported at this time), started in ALM 12.2x and later versions. the matrix of supported non HP software shows that until version ALM 12.5, only the Excel addin is supported and at that version support for the entire suite is added.
Hope this helps,