Absolutely it's possible, you just may have to write a lot your self as it doesn't look like there is a published API that's not websockets.
Have you seen this page? There are a lot of unsupported ways to interface to the board.
http://unipi.technology/wiki/Main_Page
Just a quick look at the page and source. EVOK the official API written in python is completely open source, so it would be simple to write your own C interface. It also looks like the base of EVOK is pigpio. pigpio is a GPIO interface in C, but I think it's main intent is to be used as a socket interface for GPIO.
So, dig around in pigpio and I bet you can simply use that. But my first start would be to use wiringPI, it looks like there isn't anything special about the board, it's all standard GPIO stuff that I bet you can simply access all of it with wiringPI.
A little further digging shows that an automation project called Fhem, actually uses wiringPI to interface with the board.
http://unipi.technology/wiki/Fhem_%26_UniPi
http://fhem.de/fhem.html
So, download wiringPI and it looks like with a little understanding of how the GPIO pins are connected to unipi board "features" you can simply use that as your API.