Hmm, i get you now :P
So it's only on his that the hyperlink loads the installer, to suggest that adobe isn't installed, yet running it from Internet Explorer (maybe) it boots the document straight away, knowing that it is installed.
Right, I might know what it is, but I don't use Outlook Express anymore, so I'll be able to tell you what the problem may be, but won't be able to tell you exactly how to fix it.
Go into Tools, Options, and check if it is set up to run hyperlinks in the standard internet browser. It might not know what to run the hyperlink with, because you might have two browsers with one not having Adobe Acrobat Reader, because it is a plugin for a browser when running it like this. (EDIT: I ran the program and couldn't find this...)
There would be something about this i'm sure somewhere. For example, switch it to the browser you copied the hyperlink to
If you can't find this option, does it allow you to right click the hyperlink, and select what program to run it with?
EDIT: With the browser you ran and copied the hyperlink to it, does it by any chance say it is not the default browser? If so, say to make it the default browser and hopefully Outlook Express will see this and run it with that browser)
Hope this helps