If Gstreamer doesn't have VA-API support, then WebkitGTK browsers such as Gnome Web and Midori use an insane amount of power, make the computer blazing hot, and grind the whole system to a near halt on some websites, such as Facebook and Youtube. I was trying to figure out what the problem was on Fedora 26 with these browsers and then found out that (1) Fedora doesn't have Intel's VA-API driver by default (but RPM Fusion's packages were on my system since I use Steam, and (2) although the Gstreamer VA-API support plug-in is available in Fedora, it's not installed by default. Installing the GStreamer VA-API plug-in got this problem under control, but is there some way that WebkitGTK could behave better without it? Firefox doesn't seem to display this sort of behavior even without VA-API support. Gnome Web turned my computer into a slide show when I played a video without VA-API.
What kind (codecs) of video were you trying to play? There's nothing WebKitGTK can do when hw-decoders are not used, in that case ffmpeg and fallback vpx decoders are used...
This seems more like a packaging/distro issue. Please reopen and answer questions in comment 1 too.