The display engine is the component that actually composes and draws what appears on screen. It takes the layout, the assets and any live data, and produces the frames, which makes it the part that determines whether a screen looks smooth or stutters.
It matters because it sets what is possible. An engine rendering a web view can do anything a browser can, including live data and animation, but pays for it in memory. One playing prepared video files is efficient and predictable but cannot show a price that changed a second ago. Most real products are a hybrid, and where they draw that line explains most of their behaviour.
The caveat is that engine performance is only ever demonstrated on the vendor's hardware. The same layout that runs at 60fps on a demo box may crawl on the media player actually being deployed, particularly with several independently-updating zones. Test the real layout on the real device before committing to a fleet.
Watch memory over time rather than at startup. Engines that look fine on day one and degrade after a week of continuous playback are a common and expensive surprise.