Ubuntu – Installing Intel graphics driver in Ubuntu 16.04

I have a dual Intel 6th gen./AMD Radeon HD graphics, and I have recently upgraded to Ubuntu 16.04 LTS. I was prviously on Ubuntu 14.04, using Intel graphics driver in Ubuntu 16.04, installed from here:

https://download.01.org/gfx/ubuntu/14.04/

Video acceleration worked just fine in VLC in 14.04. But, now I have several issues with video acceleration, including the inability to scale the video. So, I want to use graphics drivers provided by Intel, but unfortuanately there is no prebuilt packages for 16.04 in 01.org repositories. What should I do?

Another issue is that I no longer see propertiary drivers in "additional drivers" section of the "software and updates" utility. Is it because I am using newer kernels? Previously I could be able to see AMD propertiary drivers, and install it if I wanted, which I once did for testing, and then returned to Intel graphics.

PS: In the list provided here, I have a Gen6 Intel GPU. I have installed the 15.04 binaries, and this is the output from vainfo:

$ vainfo 
libva info: VA-API version 0.39.0
libva info: va_getDriverName() returns 0
libva info: Trying to open /usr/lib/x86_64-linux-gnu/dri/i965_drv_video.so
libva info: Found init function __vaDriverInit_0_39
libva info: va_openDriver() returns 0
vainfo: VA-API version: 0.39 (libva 1.7.0)
vainfo: Driver version: Intel i965 driver for Intel(R) Sandybridge Mobile - 1.7.0
vainfo: Supported profile and entrypoints
      VAProfileMPEG2Simple            : VAEntrypointVLD
      VAProfileMPEG2Main              : VAEntrypointVLD
      VAProfileH264ConstrainedBaseline: VAEntrypointVLD
      VAProfileH264ConstrainedBaseline: VAEntrypointEncSlice
      VAProfileH264Main               : VAEntrypointVLD
      VAProfileH264Main               : VAEntrypointEncSlice
      VAProfileH264High               : VAEntrypointVLD
      VAProfileH264High               : VAEntrypointEncSlice
      VAProfileH264StereoHigh         : VAEntrypointVLD
      VAProfileVC1Simple              : VAEntrypointVLD
      VAProfileVC1Main                : VAEntrypointVLD
      VAProfileVC1Advanced            : VAEntrypointVLD
      VAProfileNone                   : VAEntrypointVideoProc

PS2: The problems with VAAPI support on Intel drivers seem to be widespread. For example, see these:

https://github.com/mpv-player/mpv/issues/941

https://steamcommunity.com/groups/homestream/discussions/1/616199736997712785/