You dont need to reinstall, you just need steam to be recognised the new OS. Try this first Old man, here what i do, I personally never use steams back up function as I do the following manually and it works everytime.
1) Install the latest Steam and make sure that it is NOT running. (Look in your Task Manager as the icon isn't always visible in the System tray)
2) Extract backed up Steam folder over the newly installed Steam area.
3) Delete the platform.gcf file in the steam\apps folder.
4) Restart Steam and login using my Steam account details.
5) Steam will now update itself again to the latest version and all your apps should still be there.
In your case did you back up and then move over to the newly installed windows or did u just upgrade xp to Win7? If you just upgraded then i think you can just do step 3 onwards.