If you guys like retro games, here is a free remake (by the original developers) of "Buzz Aldrin's Race Into Space" from the mid-90's.
Main page and manual:
https://www.raceintospace.org/
If you don't want to search for it from the main page, here are the official executables on SourceForge posted by the developers:
https://sourceforge.net/projects/racein ... Space/1.1/
It is a turn based space simulation strategy game, where you take control on either the USA or the USSR space program, and it can be very challenging (reading the manual is a must).
If you use Windows, you may have to use DOSBox with this, but as I use Linux, I just built it from source.
This is the only game I encountered with so far, that has the most historical feel in scope of the Space Race.
If you know any similar (besides of course KSP or a modded Orbiter), please share!
Have fun!