Race Into Space is the computer version of the Liftoff! board game by Fritz Bronner. It was developed by Strategic Visions and published by Interplay as a disk-based game in 1993 and a CD-ROM in 1994.
The "remastered" open-source version was released in 2005.
You play the director of the U.S. or U.S.S.R. space agency, preparing and launching missions, researching new technologies (better rockets, manned spacecrafts), managing your astronauts/cosmonauts until you finally land on the moon, hopefully before the other space agency does.