Leonardo with BLE

I'm trying to use this DF Robot Gamepad which contains a port to add a Bluetooth module. Essentially the underlying board in the gamepad is an Arduino Leonardo and I'm using the Bluetooth Bee module to cough hopefully cough transmit the various buttons/joystick information to an Arduino MKR Wifi1010 board.

I wanted to start simple by simply trying to create a peripheral service characteristic which (broadcast by the Leonardo gamepad) and then have my Arduino MKR board receive the characteristic. I started by looking at this example and the only thing I've changed is the digital pin connected to the button. The example uses digital pin 4 and I've changed this to pin 5 to correspond to the "UP" button on the gamepad. However, when I set my board type to Leonardo and then try to compile, the IDE says that it can't compile the code for the board Arduino Leonardo. I kinda assumed that if I was using a bluetooth module that I could then compile code which used the Bluetooth BLE library. But this doesn't appear to be the case. Can anyone advise me here on how to proceed?

The Bluetooth Bee is a Bluetooth 2.0 device which is not compatible with BLE devices.