Cross-compiling with cgo can be frustrating at times, at least in my own experience. Since Ebitengine is a game engine, and they made this repository, I am presuming it's related.
Using Zig for Go cross-compilation, although quite great, isn't bulletproof. Finding the right CC/CXX incantation can be fairly tricky, the articles on this are not super up-to-date, and you need a copy of the macOS SDK[0] if you intend to cross-compile for macOS. You may also run into a few scary linker warnings and need to figure out the right Go build flags.
I definitely think Zig and Go can be best-friends, after all they share so many similar qualities and seem quite complementary to each-other. It's definitely possible to get Go<->Zig CGO cross compilation working (I did so for Sourcegraph); But Zig needs a little more love before it'll 'just work' as claimed for the Go use case, so best not to claim otherwise until then.
Pure Go? don't need anything else beside the Go compiler.
If you can avoid CGO, Avoid it.
When cross compiling with cgo you need a C cross compiling toolchain for the target platform installed with the right libc, etc. It is not impossible and that is how C/C++ is always cross compiled, but it is much more hassle than compiling pure Go.