Homebrew generally only provides compiled packages for three macOS versions. Now that there is mojave, it means support for 10.11 El Capitan is being dropped. That is why the travis builds are failing.
Unfortunately, I don't have time to do the necessary work. If there is anyone here that does have time and wants to take on the task, I can give instructions on what exactly needs to be done. It will require some development work because last time I checked, qtwebkit needed patching to build on Mojave (maybe a simple thing, I didn't look into it).