The biggest impact is for Android. The official advisory from Unity https://unity.com/security/sept-2025-01 lists that for desktop platforms it's more of privilege escalation instead of code execution.
On windows if the game has been registered as custom URL scheme handler it opens ways for triggering it without ability to pass custom CLI arguments.
On macOS as part of application signing macOS apps also contain permission manifest. So in theory if a user runs a malicious app (which for some reason is properly signed but with limited permissions) it could leverage a vulnerable game to run in the context of slightly more permissions but still as the same user.
On Linux in most cases anyone able to pass cli arguments could also run code directly with same privileges. I guess if the game executable was marked as setuid. That seems unlikely.