One of the things that trouble me is that I failed to find anything related to security in that website, it sounds like a well intentioned hobby project that got exposure.
Yes, it opens a port and exposes a service. Knowing which port it uses is possibly very easy if you download it yourself, it is possible they don't randomise the port in use but even if they did a port scan would discover it fairly quickly. Then its a matter of playing with packets and see what sort of authentication is in place.
The immediate risk that I see is that the computer would shutdown or restart before you want it to happen, it seems however that this is targeted at home users where this wouldn't be much of a problem, even if it can be annoying I don't see a direct relation towards data loss or compromise, partly because it runs on Java and it is a sandboxed environment.
If you are concerned about security and need to use this tool, I would recommend not having the PC connected directly to the internet, you should still be able to use the program from within your home network, and if you want to be completely safe you can disconnect the internet cable from your home router.
The usual home safety recommendations apply, use strong encryption on your connections, if available only allow connections from specific MAC addresses...