"Zero-K.exe" is a mono (.net) executable and will run with whatever architecture your Mono is compiled for. If you have a mono installed on a 64-bit linux, it will run 64-bit.
"Zero-K_linux64" is a mkbundle binary generated with mono on a 64-bit linux. Basically it's the above program bundled with a 64-bit Mono so that the user doesn't have to install mono.
Both are irrelevant, however. The meat of everything is the Spring engine, which you will find at "engine/linux64/103.0.1 maintenance-gibberish-abracadabra/spring" subpath of your install.
That should be an ELF64 binary.
Tl;dr don't worry and assist the bomb rush.