One does generally not use the term ROM for CD or DVD ROM games. It's mostly used for cardridges and media types that cannot normally be read by a regular computer. When it's a CD or DVD, one would usually refer to them as CD or DVD images.

And the delete after 24 hours thing is indeed a legend. When you download the game, it is copied off the server, and the copyright is therefore broken. It doesn't usually matter with really old games anyway, because the company that made them probably isn't making money off them anymore anyway. This doesn't apply to most Final Fantasy games anymore though, because S-E started re-releasing just about every FF game made.