While DRI3 appears to be in good shape with the latest X.Org Server series and Direct Rendering Infrastructure 3 is even mandated by the Intel Mesa Vulkan driver, DRI2 is still the default with the xf86-video-intel DDX driver, similar to the situation in the Radeon DDX driver as well.
For those wondering about the performance impact of enabling DRI3 rather than using the default DRI2, there are some benchmarks in this article of DRI2 vs. DRI3 rendering using an Intel Core i5 6600K "Skylake" system with HD Graphics 530. Besides potentially faster performance and being a requirement for the Intel Vulkan driver on X11, DRI3 can reduce tearing and provide other benefits too.
Pretty normal system used for testing. The Ubuntu 15.10 system was upgraded to Linux 4.5 and Mesa 11.2-devel.
Adding Option "DRI" "3" to your Intel driver section of your xorg.conf/xorg.conf.d is all that's needed to switch over to DRI3. You can check your Xorg.0.log to verify DRI3 is active.