Keep in mind that you are not seeing a complete "half" of the earth in this picture. As your distance increases, the effective horizon encompasses more of the surface. Only at infinite distance would you see exactly half of a sphere (mathematically speaking).
Try taking a picture of your globe closer and closer to the surface and watch as less of the surface is visible in each.
I have been working on a realistic scale space simulator (working title, Space Freighters) that I like to describe as a "truck simulator in space." [0] The focus is currently in creating a simulator with realistic spaceflight physics (I am an aerospace engineer by day), that also allows you to bend some rules with options for FTL travel. I am striving for a calm gameplay similar to the truck simulator franchises in which the player can deliver cargo and take time to admire the universe around them.
The project is still young, and I do not have a lot to share at the moment, but if you are interested, you can follow along on the subreddit below!
I am working on exactly this with an engine I have developed in my spare time. So far, I have implemented a realistic physics model for both flight through a fluid (based on stability derivatives, much like Flight Simulator) and for space travel (currently Newtonian). Although I hope to one day support a large procedural universe, currently only a Terra type world with an Earth-like moon are supported.
Try taking a picture of your globe closer and closer to the surface and watch as less of the surface is visible in each.