I'm going to guess that you are (or were) running Services for Macintosh on the original server?
What seems to have happened is that the type and creator codes for those Quark files got lost in the move. (The type/creator codes are used to associate files with applications on the Macintosh, in the same way that extensions are on PCs.) Windows Server will keep track of these only while they are stored on a "Macintosh-accessible volume" directory on a server running SFM. If you burn files to CD, or move them to another directory on the Windows server, the type/creator codes are stripped out. Likewise, if you transfer them using FTP or Windows' native file sharing, the type/creator codes won't survive the trip.
You can associate a Windows type/creator code to a file on the server by following
this procedure, but you'll need to know the codes for each file type. (For Quark they are Type: XDOC and Creator: XPR3)