Hi Jagsfish,
Welcome to Vista Forums!
If you did a full system recovery to factory conditions, then unless you had a complete image backup, the only thing your full backup (unless you used Easy Transfer) would have successfully restored would have been your data. Even with Easy Transfer, the programs would need to be re-installed as would all the updates (unless the programs came installed with the computer and were on the Recovery Disk or Recovery Partition). If you did do an image restore (your system specs indicate a version of Vista without complete image backup capability unless you've installed a 3rd party program to do it) and all other programs work but it still lost the outlook.exe file (and maybe only that file), the solution is pretty much the same.
I recommend you re-install whatever version of Office you have (or at least the Outlook program if the other Office programs are working fine) and that should restore the .exe file (and any other missing Office or Outlook files as well as registry entries) and get things back to normal again (though you will probably need to reset the settings for your e-mail provider and to link to the correct PST files that you backed up). If, on the other hand your system came with a trial edition of Office and you never actually purchased the product, then a different solution may be required (perhaps doing another system recovery to see if the file properly transfers this time, or the one recommended above to read the PDF files and another to select an e-mail program - possibly purchasing Outlook or choosing some other option - several are provided in a link posted later).
If you did buy Outlook and/or Office, I suspect you'd rather that Office Outlook be working than use a different program altogether that almost certainly isn't as functional or good as Outlook (and may only read PST files but not actually send and receive emails or do most of what Outlook can do). Just be sure this is the only program with problems so you know if you need to install just Outlook or the whole Office suite.
I hope this helps.
Good luck!