Lightning strike in Peru - people falling over

Video here:

When the lightning hits (and kills) the player, a number of other players quite far away also fall over. Is this because of the potential difference as the lightning bolt dissipates in the ground? It seems like they are pretty far away to be affected by that.

Yes, it’s ground current as described here.

The usual term is step voltage, i.e. the voltage between two points a step apart. It matters for lightning strikes, but also for malfunctioning electrical equipment that’s applying high voltage to the ground:

“Step voltage” is the voltage between the feet of a person standing near an energized grounded object. It is equal to the difference in voltage, given by the voltage distribution curve, between two points at different distances from the “electrode”. A person could be at risk of injury during a fault simply by standing near the grounding point.

Step voltage is one of the ways that people standing under trees get killed when lightning strikes the tree. The current flows down through the tree trunk and dissipates radially through the earth, creating a step voltage that electrocutes anyone standing close to the tree without the lightning ever actually having struck the victims directly.

It’s also how large herds of animals can be killed with a single lightning strike:

This speaks to the extremely high voltages and currents that are present in lightning strikes. We build electrical machinery that operates at tens or hundreds of thousands of volts, but lightning operates in the range of millions of volts.

I can’t see any video at the OP’s link, so here’s a direct YouTube link.