Video: Did I mention it's illegal too? Because it's super illegal. While everything about this video screams "Russian prank!", charging a phone off the rails seem scientifically legit. Many lines run a low voltage through their tracks so that stations can determine the location of individual trains -- which is also why this is so dangerous. Not only would someone charging their phone this way risk getting run over, but interrupting the rail power likely sends false information to the signalers who control train patterns. Luckily, this experiment was allegedly "performed under the supervision of an experienced railway worker".
Although the power is inconsistent, the video's creator used a rectifier to keep the tracks from frying his Nokia brick.