The only safe way to protect from a nearby lightning strike is to unplug the game. A surge protector is worthless for a close hit, surge protectors work for small spikes. Shutting off the circuit at the load center is better than just switching the game off, and if you have a ton of games this is probably what I'd do. But unplugging is still the safest. I unplug my games when storms come through.

The switch cuts all power to the game, there is no power draw when switched off, other than from the battery to keep the memory in the RAM.

A wall switch will do the same thing as the switch in the game cabinet, and it would add another layer of protection between the game and any spikes.

As anyone who has been shocked by static electricity can attest, if you have a high enough voltage, you can get a spark that will cross a boundary and conduct electricity. A close lighting strike can fry stuff that is switched off because you are dealing with very high voltages. And the gap that needs to be jumped in a switch isn't very large. It might start a fire, it might not, lightning can do strange things. I've seen stuff damaged with no other apparent harm. A buddy had his huge TV zapped a year ago. He lucked out that is was under warranty and they covered it.

We get enough crazy electrical storms where I live that I unplug my games, computers, and entertainment stuff (TV, home theater) when a storm comes through.