4017 Counter LED Shuffle By Touch
The 4017 IC is a decade counter - each clock cycle causes it to shift the positive level to the next output. Pin 14 is the clock input.

Fingers are complex and multifunctional. Like any other part of the body, a finger can serve as a weak signal source. I slowed the video and counted between 10 and 20 switches in a second (it is hard to tell if certain diodes are lighting up or merely reflecting others on at the same time). This is faster than I would expect from the 4-5 rising slopes found in 70-beat-per-minute electrocardiogram, so other noise is probably responsible. There are dozens of other distinct signals and noise sources in the 1's and 10's of Hz. As the blinking shows, the "clock" signal is irregular, which is how it can produce a pseudo-random signal despite operating at near-human speeds where careful timing might otherwise allow for manipulation.

The body is a weak signal source, but the circuit will float with it if nothing (ground or some sort of induced voltage from "something electrical") holds it back. This would prevent the voltage between the clock and ground pins from crossing the threshold at which a  rising edge would be detected.