I'm trying to interface the sense HAT with a PIC24 based non-Raspberry Pi motherboard. I'm not good with computer hardware and standards so I don't know what other information to give for a useful answer. The purpose of this is to use the sensor package of the sense HAT for a balloon launch to gather telemetry data.
The sense HAT has a couple of sensors, all of which are interfaced over I2C. The sensors are LPS25H(pressure/temp sensor), LSM9DS1(IMU), HTS221(Humidity and temperature sensor) and LED2472G(Led Driver). More details on the pinout are here.
Now, if you connect to the Sense hat from another MCU via I2C, all the sensors would be available on the I2C interface, however you will have to write libraries to get them working if the libraries are not already available for your MCU. Libraries for these sensors are available for Arduino, so you can port them to your platform. Here's the library for the IMU as an example. If you have to port them and have not done it before for another sensor, it might be a little tricky to get it working.