The announcement seems clear that all files that were available will still be available, but will have to be downloaded to run.
This may take some effort, though. You can’t browse a directory that’s offered this way (e.g. dl.dropboxusercontent.com/s/4e76m6zlvdk2z0g/ doesn’t list files). So you’d have to look at the HTML, extract the list of relative URLs, and download each of them.
(This is already true; it’s not going to get harder in October.)
I should also mention that I still run plover.net, an IF-mostly-focused Linux server. If you need a place to host twine or quixe or similar works, a free plover account is yours for the asking. You’ll need to learn a little about setting up your public_html folder and if you want a domain tied to it, that will require a little extra time on my part (or my sometimes-helper vimes). There is a donation page, but I don’t necessarily need donations. Some people feel it’s worth $5/month though so they chip in. The server is a linode server and I think the bill is around $250/year.
The only thing I can’t handle is any super high traffic, high volume stuff (I used to host a mirror for the archive and ifcomp downloads and had to drop/relocate those efforts). But IF stories are easy-peasy.
To pre-answer one obvious suggestion: the IF Archive is not really set up to handle playable Twine games. While we haven’t made it a hard policy, we prefer HTML games to be uploaded as packages (a .zip file) so that we can stick to “one game, one URL”. And also to avoid being a front-line “play all games” site, which would increase our bandwidth usage.