It’s either an idiosyncrasy of English, or possibly of human nature: the only way to arrive at being “amok” appears to be by running. It’s been like that ever since the 1600s: “Like a raging Indian..he runs amucke (as they cal it there) stabbing every man he meets.”
The word comes from Malaysia. When the Portuguese arrived (actually in the 1500s) they encountered the idea of an “amok,” which was described in 1516: “There are some of them who..go out into the streets, and kill as many persons as they meet..These are called Amuco.” It wasn’t too long before “amok” (or “amuck” or “amucke”) was paired with “running,” and that was that.
The original word in Malay, “amoq,” had pretty much the same meaning as “running amok” has for us today. The Marsden Malay Dictionary defines “amoq” as “engaging furiously in battle, attacking with desperate resolution, rushing in a state of frenzy to the commission of indiscriminate murder… Applied to any animal in a state of vicious rage.”
An odd thing about the English phrase is that you might “run amok” regardless of your means of conveyance. A driver in a demolition derby might “run amok” even while sitting down the whole time. You can even imagine the pilot of a military plane “running amok” without setting a foot on the ground, and likewise for a ship or even submarine.
In fact, as W.L. Lindsay observed back in 1879, running amok” doesn’t really have anything to do with moving at all: “Thus the running amok…is a peculiar form of human insanity.” Nowadays, of course, running amok is quite toned down from the original “murderous rage” sense, and gets applied to all sorts of things that don’t amount to much more than breaking a few rules. The spelling has also never quite settled down; you can find both “amok” and “amuck” all over the place. But they’re quite well behaved — not running amok at all.