It's now a Chrome extension; I submitted it to the Chrome Webstore (which will take several weeks to be approved) but in the meantime you can download it here: https://github.com/alexyorke/youtube-subscriptions-exporter/releases/tag/v1 . You'd have to unzip it and load it unpacked from the repo as I can't digitally sign it.

I did a lot more testing and it "just works" in Chrome without having to resize your browser window or clicking on anything first. It also "just works" in Firefox (but still needs to be made into an extension) but I haven't tested it in Safari yet.

Edit: the next steps after this (which I have not started yet) is to make a social-network out of it is to monitor the HTTP request that corresponds to YouTube downloading the list of subscriptions and extract and parse the contents. This is possible to do (I found it manually using the network inspector) but is more involved. This would mean that anytime you visit youtube.com it could automatically check your subscriptions, optionally upload them to a server to compare with your friends.