First, DevOps is a journey, not a destination. Not every organization approaches similar problems with the same solution; while automation is a component of a DevOps platform, it's not the single defining characteristic.
The role and responsibilities of QA professionals haven't really changed; they're still responsible for validating that code is ready for release. What HAS changed is the focus on both automation and smaller releases. Much like operational roles, QA staff should now have the opportunity to focus on adding additional automatic quality checks into the development life cycle.
In a shop with a mature CI/CD pipeline, QA becomes more about designing great tests, and letting the software do the actual heavy lifting. As Tensibai commented above, "some QA tests can't be automated" (yet), so there will still need to be some engineering responsibilities, but the goal should be to utilize automation in every aspect of delivery in order to facilitate adding additional quality.