Yes - no one can download it anymore. The torrent site acts as "bridge" to enable the peer to peer content sharing.
"someone who previously downloaded the file still has the .torrent" - Well, this person has to UPLOAD a NEW torrent file (created from scratch with the file or files he downloaded originally), upload that torrent to the site as NEW and only then other users will be able to download the torrent and hence the content.
Last but not least, if the site took down the torrent, it is because of banned content or a formal complaint or a DMCA violation, so a new torrent won't last long up in that site... There is always a reason.