Logo is a computer language originally made for grade-school students, so it is fairly simple to understand. To run Logo programs, you need to install an interpreter.
FMSLogo is a free Logo interpreter for Windows being maintained by David Costanzo. Asteroid Miner requires FMSLogo 6.13.0 or higher.
I've tested FMSLogo-6.27 in Linux using Wine-1.3.30, and it seems to work fine.
If you want to know more about this game, take a look at the readme file.
Download Asteroid Miner