The server isn't properly configured. It's sending the zip files with an incorrect content type, so that if you try to load them normally they display as text. In addition, it gives you "file not found" if you try to load them without a referrer link from their site; normally every time you follow a link from page A to page B, your browser sends a line that says "Referer: [url of page A]". Several browsers do not send this referrer information when saving a file, so right-clicking the link and doing Save As will not work, either.
Left-click in Internet Explorer will probably work because Internet Explorer is programmed to completely ignore the content type when accessing a file with a known extension (.zip).
I have previously been able to get around download sites that check referrers using the command-line utility wget, but "wget --referer=http://hotdog003.fchost.us/Download.htm http://hotdog003.fchost.us/binclock.zip" fails with a file not found error too. I tried the same with a faked useragent (made to look like my web browser) and that also failed, so they're obviously checking something else, and I have no clue what it is or why I was able to left-click and see the file's contents.
I suggest running away from this web host as fast as possible.