I don't actually know what it is o.o Although, looking at an ASM version, I am assuming it is a racing game? The other project was started a few years back by calc84maniac, but he hasn't had much time to get more done. For now, it is just some pretty screenies.
To do this in BASIC would be awesome :) You would have to use relatively low graphics, to keep some speediness, but otherwise, the physics should be doable! You might want to take advantage of some ASM programs to decrease your RAM usage, too. For example, if you are going to store tracks as matrices, it might be better to use an asm program to write to bytes as opposed to using an OS matrix (which is 9 bytes per element). Alternatively, you could probably draw an image and then use pixels for collision detection. As well, you could use lists to keep track of AI. What might be really difficult, though, is getting the AI to make decisions. You would have to make it "see" the barriers (like other cars and walls).
:D Good luck!
Edit: Also, if you want to see the ASM version screenies,… http://otbp.tifreakware.net/phpBB2/viewtopic.php?t=217&sid=5f948245296531d6a643b006201ff21e
And believe me, if you code this in BASIC, we all know the graphics won't be like that ^. So instead, I would not focus on the graphics too much and try to get the basic engine written. Then, if you think you can add some extra graphics, go for it!