What happened after you changed the target program (Windows Installer)? Does Windows Explorer list the file as Windows Installer Patch?
What is your Windows version?
Meanwhile, if you need Reader 10.1.2, try downloading the full installer (.exe) from http://get.adobe.com/reader/enterprise/
Try using the registry fix provided at http://www.sevenforums.com/tutorials/19449-default-file-type-associations-restore.html.
Scroll down to registry fix for .MSP files, download and run the same.
Hopefully if should solve your issue.
I used the shell syntax of the Windows Installer: msiexec.exe /p path\file.msp
That would work as well.!!
But in case, you want to ensure that double clicking also produces the correct results, you can use the above mentioned registry fix.