Is there any way to request a stanford alumni interview?
No there is not. If you applied and your state or international location is on the list of places Stanford offers interviews you will get invited to an interview provided there are enough interviewers. If you do not get invited to an interview it is simply because they were short on interviewers for your area. There is nothing you can do to push the process along or wrangle an interview: you will either get one or not, depending in the availability of interviewers.