The AH Corsairs aren't packed in an installer EXE. The download is just a ZIP archive with the aircraft folders inside. These folders will need to be placed in the game manually.
I am guessing that you have the CFS3 version? If so, follow these instructions...
(The steps should be the same for the FS9 version too.)
Once you've downloaded the ZIP and received the password email from Ickie, you can unzip the archive into a temporary folder. You should find two folders in there, one is HELP and the other is AIRCRAFT. Right-click on the AIRCRAFT folder and choose "copy". Then navigate to your main CFS3 folder and right-click/"paste" that AIRCRAFT folder into your main CFS3 folder. This should place the plane into the proper place.
Let us know if it works out for ya.