No. There are some that actually use the Raspberry Pi hardware, such as PiFM[0]. Others merely use GPIO, which of course can work on a number of other SBCs (eg a Beaglebone Black) or anything with GPIOs. The only Raspberry Pi specific thing here is how it connects to the webcam, because the Raspberry Pi doesn't expose the camera as a standard v4l device, they have their own way of doing it.

[0]: https://github.com/ChristopheJacquet/PiFmRds