The \new folder should be removed during the install (i.e. the path trimmed when it is presented) and it will proceed correctly. It would be worthwhile taking a backup of the Steam install directory for Warthog first.
For info, I downloaded the full install and ran so I had both a Steam and a non-steam version; it seemed to install correctly without me needing to do anything extra. WFIW, doing an A/B comparison between the 1.1.0.8 Steam version and the 1.1.0.9 full install, I noticed that there was a 15-20% drop in performance, hence the suggestion to take the backup in case this installation approach method is sub-optimal for some reason. I'm about to apply the patch to the Steam version shortly and will report back.
First post for me here ....
Edit: I've applied the patch and can confirm, for me anyway, I get a significant drop in performance applying the patch to the Steam version. Takeoff training mission drops from around 52fps to 43fps when it starts up.
Second Edit: The patch reinstalls the graphics.cfg file which I'd made some changes to. I've added these back in and all is good.