I think most of this is attributable to the ergonomics of compile-time expressiveness. C++ can effortlessly do things that require mountains of ugly boilerplate and macros in C or Rust. In principle they can express the same things but no one wants to write or deal with that ugly boilerplate so the equivalency is never realized in real code bases.
Zig is interesting because it slots in as a C-like language with a competent and expressive compile-time story. I don’t use Zig but I recognize its game.
If anything, Rust has the potential to be more performant than C due to its aliasing rules (C has `restrict` but it's rarely used, standard C++ does not have even that). The current perf stats show it does make Rust code faster but just a little bit, although we don't utilize the optimization potential currently (LLVM does not do many possible optimizations here, and `noalias` is weaker than Rust's aliasing rules). It can also affect autovectorization, and if it does the effect could be dramatic.
Compounding on this, Rust is also unstable underneath, since there is no public, stable contract for carrying high-level semantics from HIR into MIR. Because these high-level invariants are lost during compilation, the compiler cannot easily use them to prove and eliminate low-level safety checks. But even if the frontend was perfect, Rust relies on LLVM's language-neutral SCEV, which operates purely on low-level math and cannot reason about high-level language semantics.
Ultimately, a lot of things would need to change for Rust to pay no performance for safety features.
There are techniques to minimize the perf loss, though (safely), and of course you can use unsafe code. If you do it smartly, in the vast majority of cases bound checks do not matter (in fact, even in C++ there is a push for a hardened standard library that does bound checks, and e.g. Google uses that).
Rust will never include full proofs, but it might include ranged integers which can minimize bound checks even more.
let mut tab: [usize;100] = [0;100];
...
for i in 0..101 {
tab[i] = i;
}
Even if the panic message would not include the index, LLVM was unable to do that if the previous iterations had side effects (for example if `tab` is not a local variable).
But no, "memory safety" includes most of the things discussed on the slides, and those number are for bounds checking only.