I spent many years working in the video graphics design industry. One of our problems is the opposite problem, that is, we have limits on how much electromagnetic radiation our products can produce. Before we can ship any new design, we have to test it to make sure it meets the limits. (The tests are done on samples, not on every item shipped.)
The limits have to be low enough that the equipment doesn't cause interference for radio and TV. You would think that would eliminate the problem, but in fact, all equipment puts out some unwanted radiation. So I have no doubt at all that the radiation is there to be analyzed.
Display systems have a clock that moves the data. On some modern systems the clock is "spread spectrum" but it should be possible to figure out the spread algorithm. It's not like they design these things to be impervious to decryption, instead the purpose with spread spectrum is to spread the noise produced by your equipment over a wider frequency range. This lowers the spikes in your noise spectrum and keeps them under the limits. In other words it allows you to radiate more while still staying in compliance with government limits. See the wikipedia article:
Spread Spectrum clock signal generation
If someone wanted me to do this, I would try to design an antenna that (a) Is very very directional. That way you can point it at the device you want to receive from. (b) I would work hard on understanding the interfering signals and subtract them from the signal, either digitally or in analog. (c) Understand the spread spectrum of the target device and design a system to cancel it out. And just typing this, I've already got some ideas that I'm sure would work.
The more general problem, where you don't know what make of equipment you're trying to receive from, is going to be a lot tougher, but it should be doable by the guys in black.
So I have no doubt at all that, given a paycheck and some time, I could extract those pictures.