Hi Mike. There's a couple of issues here.
First, matching on SITE only matches on the domain part of the URL. So something like
http://website.com/badprogram.exe would not be picked up by a site match as it would only look at website.com. What you would want is a URL match. I have tested a setup as you described with a URL match and it is blocking download of .exe files with one caveat.
As is with the mozilla example you gave, HTTPS requests pose problems. HTTPS sets up a connection between client and server and from then on the content is encrypted, which means we don't know what requests are being sent from the client browers and therefore there is no way to know if they are asking for an EXE.
WinGate 8 introduced SSL inspection which might solve your problem however. You create a certificate, enable SSL Inspection in the WWW Proxy Server and install the certificate on the client machines (Or use Active Directory policy to ship it out). Then, WinGate will be able to inspect the traffic and block traffic. Again, I have just tested this with Categories, Data List and Access Rules and I could successfully block the mozilla .exe download.
If you have current version protection you should be able to upgrade to WinGate 8 for free.
Let me know if you need any more help.
Aaron