I had to run make on the uncompressed folder. Perhaps the build-essential package doesn't come with NASM in Ubuntu? I'll need a bit more info on the error if you want me to try and help you :)
The parent commenter seems to have figured this out, but to clarify a bit for posterity: build-essential does not come with nasm on Ubuntu (or upstream Debian, AFAICT). It has to be installed separately for the Zenbleed PoC to compile (if not already installed).
After extracting the POC and installing build-essential, I still get this:
nasm -O0 -felf64 -o zenleak.o zenleak.asm
make: nasm: No such file or directory
make: ** [Makefile:11: zenleak.o] Error 127