With c2rust it wouldn't. It would likely be slower in some cases due to added checks for, say, buffer overruns.
But that's not the point. C2rust code is not "idiomatic". You get weird, unsafe Rust code full of potential side effects. The idea is to provide a means for you to start rewriting things in ways that make sense in Rust.
Would the final code be faster? Harder to tell. Maybe, maybe not. It depends on how well it's implemented, what kind of clever constructs are applied, what the game's bottlenecks are, etc.
And yet, I don't think that matters much either. Games shouldn't be bound by CPU as much nowadays unless they're doing massive simulations that are likely not language constrained. So it would be the wrong comparison to make IMO.