"supports 4k" means the device is capable of outputting a video signal at a max resolutyion of 3840x2160 or higher
that doesn't mean it can render 3d video at the resolution
so "supports 4k' in this case means it'll run microsoft word at 4k
intel graphics aren't even made to ruin 1080p
forget, even current gen consoles, which are made to play games, struggle to run 1080p. Most games are 720p 60 fps or 1080p 30fps
then bumping up to 4k means you have 4 times as many pixels to render, so expect your FPS to drop down to a third or even a quarter of what it was.
That all being said, 4k will still be fantastic for non-gaming related things. (I love my 1440p monitor for photo editing, gaming on it was honestly an afterthought)