Rather than trying to run the compiler itself on a given platform, I'd recommend cross-compiling binaries from a known platform. I'm not an expert in this aspect of Rust, but here's some example Rust code that targets the PSP: https://github.com/luqmana/rust-psp-hello (AIUI the magic is in the psp.json.in file, which communicates a target specification to the compiler).
Feel free to come ask in #rust on irc.mozilla.org if you need some experts to consult!
I have a VPS running x86_64 Debian unstable so I installed Rust on it now.
I compiled an hello world on the VPS, the content of which is:
fn main () {
println!("hello world");
}
using
rustc main.rs
and the resulting binary ran on the VPS and said
hello world
I went to the example Rust code you linked that targets PSP and had a quick look at it but it was kind of a lot at once so I went looking for alternatives and found https://github.com/japaric/ruststrap which seemed promising but the README was not very clear and the archive hosted by that person is from 2014-12-17. I cloned it to my VPS and attempted to run the ruststrap.sh which it didn't want to unless it was root so I let it be root but it ended with
+ apt-get install -qq g++-arm-linux-gnueabihf
E: Unable to correct problems, you have held broken packages.
So I'm not sure if I was supposed to run that on x86_64 or not or if maybe I was supposed to run something else first. My VPS is a bit of a mess so that could be the reason also.
I am going to go back now to the example Rust code for PSP you linked and look more at it, it seems to be the most promising at this point (though it will be a bit inconvenient for me in the long run to do any development on the VPS instead of locally.)
Feel free to come ask in #rust on irc.mozilla.org if you need some experts to consult!