Tell us what you are trying to do?
I would like to know if it's possible to use the [wpv-post-previous-link] and [wpv-post-next-link] functions and sort alphabetically instead of by post date. And if not, is there another solution that would work? Thank you.
What is the link to your site?
nakwpn.wpengine.com
Those shortcodes are just a way of inserting the links generated by the WordPress functions such as get_next_post_link(), where next and previous are determined by the post date.
If you want links to the next alphabetical post you will need to use one or more Views.
The easiest solution would be if you are displaying a single post not at the usual URL for single posts, but at a static page that includes a View to output the posts in alphabetical order, and which includes pagination where only one post is shown per page, and you can then add the navigation controls to move back and forth.
A more complex solution would be to use the normal URL for single posts and in the template for such posts create custom shortcodes to display the links. You can't readily create them using Views, the logic required is too complex.
So the first question is does displaying the single posts at a static page using a View sound like a viable option?