If programs, such as video games, are mathematical objects, then the world is one too. But, of course, they are not. They are physical objects distributed in space and in time -- hence why people play them.

ED's discrete mathematics idealism here is the windmill he's tilting against. This is the origin of the very confusions he's annoyed with.

No, programs are not abstractions, and that is why almost every programmer bothers to write one.