During the move to TreeSprite's server the files got transferred using FTP in ASCII mode instead of binary, which corrupted the attachments.
The authors of phpBB, the forum software that powered Creaturetopia, warned users in August 2011 about the dangers of ASCII transfer mode. Sadly, it was too late. The move of Creaturetopia was in 2010.
The most interesting parts (emphasis mine):
phpBB Group wrote:
If a file is transferred in the wrong mode, it can become corrupted. For text files, it usually doesn’t matter what mode you’re transferring them in unless you’re expecting to see how the file actually looks on the server. For any kind of binary file (images, executables, etc…), transferring them in ASCII mode will ruin them. Your file had an 0x0A (LF) in it? Well, now it has 0x0D 0x0A (CRLF) in that spot. That was an image? That’s unfortunate, because now it’s going to render differently (if at all).
(...)
Why do attachments break? For your own safety, uploaded attachments have their names changed to a hash and their file extensions are removed. (You can read about a few of the reasons for our attachment handling here.) Most FTP clients adhere to their list of ASCII extensions and upload everything else in binary mode. Some clients though, like FileZilla, default to transferring extensionless files in ASCII mode.
(...)
Recovering the files is not possible at this point. The only option is to change the transfer mode and download them again if you still have access to the originals. “But can’t I just re-upload the files and let the line endings get converted back?” Unfortunately, no. Existing Line Feeds would have had a Carriage Return added in front of them, and existing CRLFs would have been left alone. Uploading it would convert both the new and the previous CRLFs to LF. The file is lost.
It seems that it isn't possible to repair the attachments, sadly. 
EDIT: I found a solution! It seems that at least zip files can be repaired using fixgz by gzip.