I trawled the entries for the Hackaday 1k prize - so you don’t have to. I looked for a retrocomputing angle, and there was plenty to find: 17 projects being a mix of hardware and software projects, for Z80, 6502, 8008, 8048, 65816. There are applications, interpreters, games. The 596 byte chess is rather a feat.
Here’s an index, grouped by the flavour of microprocessor:
Chess on the VCS (Atari 2600) is always impressive!
For those who don’t happen to know, the VCS has only 128 bytes of RAM, which doubles as the processor stack, inside its I/O interface chip (RIOT) and outside of this no dedicated memory at all. Also, there’s no video memory (video is produced on-the-fly line by line), so the bit of memory, there is, is also needed for video generation, like storing memory offsets to access sprite graphics, etc. This is a limitation probably more severe than confining the program to 1K of ROM.