For animations there's also the
Bit Blit algorithm. You can watch
this YouTube video by Computerphile for a good explanation on how it works.
It is a more general algorithm and I think it will be slower for this particular game. Still, it's interesting and historically important. Some graphics and game-oriented systems in the 1980s and 1990s implemented it in hardware. It could be a fun project to implement as an extension to the hack machine.