Having not worked with Slackware or Gtk2::WebKit I admit I'm at a bit of a disadvantage here, but I imagine I'm not the only one. I can't seem to find a Slackware package named something like "webkit-1.0"
Slackware traditionally has only a relatively small set of packages (about 1300 in 14.2), you are expected to build and install software not part of Slackware from source. There is SlackBuilds.org, where you can find build scripts for about 6000 more packages. Download the build script and the source, run the build script as root, and you get an installable slackware package that can be installed using installpkg. If the software you want to install is neither available as a Slackware package nor as a SlackBuild script, you are on your own.
Yes, younger package systems using *.deb or *.rpm packages give quite instant results, just type sudo apt-get whatever-you-want or some other variant and you'll get it, including all dependencies. If you just want to use your system as a blackbox and don't intent to learn anything, use them. Slackware does not use or support them, and for good reasons.
A very welcome side effect is that you really learn how your system works. Slackware is - at the first look - a little bit under-documented. Apart from the documentation that comes with the system, there is a Slackbook dated 2005, and another slightly newer beta dated 2012. One of the first things to learn is how to find documentation, i.e. using man, info, and finding things in /usr/doc. Slackware comes with most FAQs and HOWTOs from the Linux documentation project.
I'm quite sure slackware does not have a webkit package, so you want to search slackbuilds.org. And lo and behold, there are several webkit packages for several Slackware releases, including packages combining webkit and GTK.
Today I will gladly share my knowledge and experience, for there are no sweeter words than "I told you so". ;-)