Hi @david,
Have you taken a look at our slash command documentation? It will let users interact with third-party systems and receive responses from those systems by typing in commands similar to /somecomannd arg1 arg2.
You'd likely need to build some sort of intermediate application to receive commands from Mattermost and then make the appropriate request to another REST service, parsing that data into the format that Mattermost recognizes, before finally responding to the POST from Mattermost. This, with incoming and outgoing webhooks, is the recommended method of integrating with Mattermost.
Also there is an existing hubot adapter for Mattermost, which I think you're already aware of.