Sitecore has previously published a CMS Performance Tuning Guide for Sitecore 6.x and 7.x on SDN. I do not see any similar content on doc.sitecore.net for Sitecore 8.x. Is most of the content in the 7.x document on SDN still relevant? Any new considerations on 8.x which have not been documented?
The entirety of the CMS Performance Tuning guide that you linked is relevant for Sitecore 8.X. The guidelines and features discussed have not changed. The underlying architecture for some of the elements have changed (such as Caching) but how you tune has not.
What's not in here are the additional performance improvements that can be done as a result of the changes in 8.2+. For example, the inclusion of Dependency Injection or the precompiling of view renderings, all lead towards improving performance of the core product.
I would expect that as Sitecore completes the documentation phase of 8.2, we'll should start to see some performance optimization documentation. If we don't though, have confidence in knowing that the 7.X documentation is still viable and relavant.
Yes, the Performance Tuning Guide is still valid for CMS. If you see the Performance Tuning Guide page you shared was updated on Jan, 2016 - after release of 8.1, and says it's valid for Sitecore CMS 7.0 or later.
Apart from CMS, if you are using xDB, then consider some points covered in - xDB Configuration Guide.