SlateKit Base is a Linux distribution derived from Ubuntu 14.04 and is using Qt 5.2 with Mesa 10.0.1. The provided web engine is QtWebKit along with the Chromium-based Oxide. The graphics stack is just a frame-buffer (provided by either KMS or uvesafb) and then an EGL surface atop that while comprising the top level of the stack is then Qt5 with Qt Quick. That's it and there's no other display server.
In terms of the use-case for SlateKit Base, "The purpose of SlateKit Base is for demonstrating the capabilities of SlateKit project. Most of the key components of SlateKit are preloaded, including the Web Browser, On-Screen Keyboard, and Input Method. I'll add Launcher and Network Manager into next release."
More details on SlateKit Base can be learned from this blog post by Ping-Hsun Chen who is the developer behind this project.