This sentence from the linked paper is informative - "When data is exchanged between the CPU and the RAM, radio waves are emitted from the bus's long parallel circuits."
For some background:
Digital circuits like computer motherboards have components called oscillators that switch voltage on and off a number of times every second. This is what "clock speeds" refers to - 2.8 GHz CPU clock speed means voltage to CPU is being switched on and off 2.8x10^9 times per second.
All components like the processors, IO buses, RAM modules, etc. synchronize their actions to the rise and falls in these voltage levels. It's a way of synchronizing their actions.
One consequence of switching voltage on and off is that electrical fields build up and collapse (voltage is a measure of the electrical field), and cause magnetic fields to build up and collapse. We lay people call "oscillating electromagnetic fields" as "radio waves". This is the origin of radio waves from motherboards.
The missing link for transmission is that like any radio transmission, it requires an "antenna" - that is a conductor of some length. There are conductors on a circuit board in the form of copper traces through which current passes. These start acting like antennas.
In this case, the copper traces connecting CPU to RAM on that particular computer are emitting EM radiation at a frequency of 1580 kHz.
So far, all there is is some EM radiation with certain frequency and an antenna to transmit it. This is just the "carrier wave". But for transmitting useful information, some kind of modulation is necessary to encode data over that carrier wave. This project uses an SSE2 CPU instruction called MOVNTDQ or _mm_stream_si128 to write to memory, with the data to be transmitted encoded as sequences of 1s and 0s with certain frequency (rate) and for a certain time period. This act of at writing at a certain rate for some time period results in switching on and off of voltages on the traces between CPU and RAM which in turn creates modulated EM radiation.
TBH, I didn't understand the details of how this project modulates the binary data over a square wave and how it gets treated as amplitude modulation by a regular radio receiver, and I request another ELI5 from somebody else to explain it to me :)