Could they though? The way I understand the answer is that the security hole happens if a privileged user which manipulates files for an unprivileged user calls

Could they though? The way I understand the answer is that the security hole happens if a privileged user which manipulates files for an unprivileged user calls access() and then open(). In this case Blizzard's application is an unprivileged user, thus even if you manage to insert yourself between the calls, you will only be able to make Blizzards application execute code. The application still runs in a sandbox so you will not get that far.