[nerv_]

вариант...

function split(src, dist, step, row, column) {
    if (row + step < src.length) {
        dist.push([
            [src[row][column], src[row][column + step]],
            [src[row + step][column], src[row + step][column + step]],
        ]);
        if (column + step + 1 < src[0].length) {
            return split(src, dist, step, row, column + step + 1);
        } else {
            return split(src, dist, step, row + step + 1, 0);
        }
    }
    return dist;
}

var arr = [
    [1,2,3,4],
    [5,6,7,8],
    [9,10,11,12],
    [13,14,15,16]
];

console.log(split(arr, [], 1, 0, 0));
console.log(split(arr, [], 3, 0, 0));