Lorna Mitchell has posted a quick checklist of things you can ask about your API to see if it's RESTful or not (five of them):

I get a lot of emails asking me to get involved with API projects, and that means I see a lot of both implemented and planned "RESTful" APIs. [...] A service of some other description may work better for other scenarios or skill sets, and non-RESTful services can be very, very useful. If you tell me that your service is RESTful, then I expect it to be. If you're not sure, look out for these clues:

• It has a single endpoint
• All requests are POSTs
• Response metadata is in the body, not header
• There are verbs in the URL
• The URL includes method names

She suggests, though, that "being RESTful" isn't a requirement for "being useful" when it comes to APIs.