If my failing memory allows me to remember that far back, I believe that Windows Me has no built in support for .zip files. What seems to have happened is that , somehow, Quicktime has been associated with .zip files on the ME machine.
The best thing is to decompress the install file on another machine with .zip support, then copy it to and run it from the flash drive. You could also install a program such as 7-Zip to decompress the file on the Me machine, but this seems an unnecessary extra step.
If what you want to do is simply and completely erase the hard drive, I would advise you to consider Darik's Boot and Nuke (DBAN), which has its own forum on this Board. The big advantage of DBAN is that it runs from a floppy or CD in its own OS, and can therefore erase the whole of the Windows Me installation as part of the single process. It is only possible to do this with Eraser if you remove the drive, place it in a caddy, and erase it from another machine, and even then it's at least a two stage process (erase files, then free space).
Hope this helps,
David