Can you show the other side of the PCB, plus the antenna and whatever that connects to??
There is nothing in the photo that I can recognise as definitely an RF part?
For a short range toy, the actual "transmitter" could just be a transistor plus a few other components, with the microcontroller modulating that.
To be honest, for your own new project, you would be far, far better off using separate MCU IC and transmitter modules, or one of the many common modules with MCU + RF system built in.
For a short range toy, modules with Bluetooth would be fine. For longer range, ones with WiFi.
Example - an HC12 439 MHz RF module can be used with a PIC or Arduino etc. MCU; they are cheap and available worldwide:
HC-12 wireless serial communication module is a new-generation multichannel embedded wireless data transmission module Its wireless working frequency band is 433 4-473 0MHz multiple channels can be set with the stepping of 400 KHz and there are 100 channels in total The maximum transmitting
The ESP32-Devkit-C - again, readily available and with lots of analog inputs you can connect joysticks to.
This has a very fast MCU module and both WiFi and Bluetooth all in the one module.
They can also be programmed using the Arduino IDE.
I'm using one in this controller just for the analog channels, plus an HC12 for the radio link:
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