It will be certainly compatible with any microcontroller. The keyword "Arduino compatible" generally means that some of the following are true (from most to least likely):
- Module likely uses 5V signaling, or is at least 5V tolerant
- It likely interfaces using one of the hardware interfaces available on Arduino (serial, I2C, or SPI)
- There may be an Arduino library available
- It may have pin layout that works as Arduino shield (but probably not, unless it's specifically advertised as a shield)
But, it may also be that none of the above are true. Sellers oftentimes use "Arduino" as a catch all keyword to attract sales without any regard how well it works with Arduino.
As you can see, none of those features mean that it is proprietary to Arduino and won't work on any other microcontroller with appropriate hardware capabilities. Whether there is an existing library for that microcontroller is another matter, you may have to implement one yourself. But most popular micros will have libs for most common types of hardware.
Your specific item listed supports both 3.3V and 5V signaling and it interfaces using TTL serial, which makes it hardware compatible with practically all general purpose MCUs.