Dear shanks: first let me say I rejoice to see you posting again, mostly because you are so well informed.
"Run amok" and "go beserk" are akin as far as meaning that the men involved exerted themselves to the utmost, and were totally indifferent to wounds inflicted on them.
But the Norsemen who went beserk did it only in battle.
The Moslems in the Philippines I believe were attacking only
those whom they regarded as infidels, and singly rather than as part of a military attack.