After further discussions with Archos, it's become clear that the Archos 704-WiFi supports wireless playback of media files only from files on a local network, and not over the Web using the Opera Web browser -- but the details are a bit odd.
To play files over the network, place them in a shared folder on a networked Windows machine. From the 704, use the file Browser application (not the Opera Web browser) and tap on Network to view available shares, listed under the Windows workgroup name. Then tap the networked machine and then shared folder name to browse and play stored media files.
However, when surfing the Internet with the Opera Web browser, there's no built-in support for playing media files over the Web. If you click on a link to a file with a known image file format like JPG or GIF, it displays the file. If you click on other file formats it recognizes like PDF and WMV, it offers to download them, so that you then can play them back locally. But if you click on a link to a media file with an unrecognized media format, the browser happily displays the contents of the file as if it was a Web page -- showing all the binary data as unprintable text. That can be a long download ... and there's no obvious list of which file types are handled in which way.
Oddly, there's no general way to check what a link points to, and then specify that you want to download the target of a link -- even though the software is already capable of downloading files. So you can view image files, but not download them; and you can download some video files, but not view them directly; and you can't download files that the browser does not recognize.
See full article: Video Players Go Wireless: Archos 704 WiFi