There's nothing anyone can do if a user installs software. UNIX design or not, if the user runs a program, it can access everything that the user can. Nothing that this malware did needed special access (e.g. root exploit).
However, this will break nearly everything – and I am rather positive that Windows offers similar security measures, if required.
The idea that all apps run under a single "user" and all share the permissions of that "user" is just how UNIX does it, not how things must work. I don't think we've figured out proper app sandboxing yet (Mac, iOS, and Android all have their problems with it, and differently) but it seems to be the way to go.
- a recent convert to Apple
Now the malware problems on both platforms rarely rely on privilege escalation. They use trojan horses instead, and wait for you to install them.