As others have mentioned, the AM radio is responding to electromagnetic radiation from the TV. Well, in fact, it is mainly responding to magnetic radiation as a result of the antenna in the AM radio being a loop type ferrite bar antenna. The AM radio is a tuned receiver, able to receive only a little 10KHz slice of spectrum at any one time, at whatever frequency it is tuned to. You will find that the AM radio will probably pick up noise when you bring it close to your PC, your tablet computer, your cellphone, your cordless phone, compact flourescent and LED lightbulbs, your TV, your stereo, your wireless router, your microwave oven, your coffee maker and pretty much anything else electronic that is switched on at the time. This is because all of these devices nowadays use digital electronics of some sort to do their thing and digital electronics tend to generate radio noise.
The reason that they are doing this is fundamental to the way they operate. Digital electronics relies on digital logic. In digital logic, the electrical signals are binary, that is they are either at one voltage or another. Logic circuits and computers compute things sequentially, and as a result, the logic signals inside them are constantly changing at high speed between one voltage and another. To work correctly, they must go from the one voltage to the other as quickly as possible and herein lies the core reason why RF is generated. When you force a voltage in a circuit to change very quickly, you are also causing a rapid change in current flow (ohm's law must hold), so in fact you are causing a rapid change in power. It is a fact of physics that such a rapid change is done by involving a large range of spectrum. What this means to the non-physics person is that a broad spectrum of harmonics are generated, in which there is significant power. All electronic logic must generate harmonic energy in order to function, and it is the hope of the designer of each product that he can keep that energy inside his circuits, and not let it get out. But this hope does not often translate to result. Because of sloppy design, and/or because it is so blasted difficult to keep the radio frequency power inside one's circuit, the harmonic power finds its way out via radiation. You will find that of the many different kinds of receivers you might have handy, the AM radio will be hit the hardest by this. This is for a couple of reasons. One is that it is receiving relatively low frequencies, like 500KHz for example. It is a fact of physics that the harmonic energy generated in electronic devices tends to be strongest at the lowest frequencies and tends to die down as the frequency goes up, although this is not a rule you can apply in all cases. AM radio is listening to a very low frequency indeed, so it gets the worst of it. The other reason is that it is AM radio, making it sensitive to changes in RF amplitude, and it is RF amplitude that is jumping up and down a lot in the radiation from digital logic, so the AM radio is designed to hear the worst of digital emissions. This is unlike, say, your FM radio which is typically not very sensitive to AM, and unlike your cellphone or your wireless router, or for that matter, your TV remote control which are operating at much higher frequencies.