It would not be hard to write a quicksort which could be automatically vectorized. For example, this is a perfectly valid partition implementation of the pivot operation.

    int partition(int[] array, int from, int to, int pivot) {
        int[] buf1 = new int[to - from];
        int[] buf2 = new int[to - from]; // buffers could be preallocated, as in the blogpost

        int idx1 = 0;
        int idx2 = 0;

        for (int i = from; i < to; i++) {
            int value = array[i];
            if (value < pivot) {
                buf1[idx1++] = value;
            }
        }

        for (int i = from; i < to; i++) {
            int value = array[i];
            if (value >= pivot) {
                buf2[idx2++] = value;
            }
        }

        System.arraycopy(buf1, 0, array, from, idx1);
        System.arraycopy(buf2, 0, array, from, idx2);
    }

It would be relatively straightforward for a compiler to automatically vectorize the two loops I've coded up. I don't know if there's one that would, but with the vpcompress instruction I think the absence of a compiler doing it automatically would simply be a function of it not being a common use case.