The hard drive is useless by itself.
If we're talking about Rust, it's an online game available on Steam (and maybe elsewhere.) From a new computer, you can simply download Steam and then download Rust again. If someone wants to play with his old account, this is trivial, but of course it can be tracked. If someone wants to start anew, they can just create a new account and purchase Rust again (either directly through Steam or through a reseller.)
Do you know much about the actual Rust game? What kind of survival skills do the players employ? Would someone who plays it a lot and then practices out in the woods be able to actually pick up useful real-life tips? Is there anything unusual in it that could be useful in finding them if they are out in wild and have managed to keep warm, dry, and fed?