/usr/include/gstreamer-0.10/gst/vaapi/ is in libgstreamer-vaapi0.10-dev 0.3.6-0ubuntu2.
This file is owned by root:root, with mode 0o755.
..
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapicontext.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidecoder.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidecoder_ffmpeg.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidecoder_h264.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidecoder_mpeg2.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidecoder_mpeg4.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidecoder_vc1.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidisplay.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidisplay_glx.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidisplay_x11.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapidisplaycache.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiimage.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiimageformat.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiimagepool.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiobject.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiparamspecs.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiprofile.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapisubpicture.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapisurface.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapisurfacepool.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapisurfaceproxy.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapitexture.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapitypes.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapivalue.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapivideobuffer.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapivideobuffer_glx.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapivideoconverter_glx.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapivideopool.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapivideosink.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiwindow.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiwindow_glx.h
/usr/include/gstreamer-0.10/gst/vaapi/gstvaapiwindow_x11.h