It looks like the PHP code is the front facing web code which then makes curl calls into the server.js code as you suspected. Presumably server.js is run using node which listens on port 8090 and exposes a few ipfs methods which just calls into the local ipfs binary on the system using exec calls.

IPFS is an interesting project and this is a pretty cool usage of it.

It's just POSTing the image to a web server running from something else.

I don't understand why they are doing dumb things like passing everything to a shell when PHP has curl support of its own, and imagemagick.

To hazard a guess, they're probably copying the file into a directory which is mounted as an IPFS FUSE server.