The main advantage I see Rust having here is making it a little easier to (ab)use the stack for temporary stuff in a way that can be verified to be safe. Nothing you can't already do in C++ at the expense of the occasional heisenbug.
Games often create their own allocators for a variety of reasons (specialized allocation strategies for speed or fragmentation reasons, adding debug statistics, enforcing memory budgets for (sub)systems, etc.) - although that's not terribly OS or language specific.
