This is where it gets tricky. Your obligations to your employer don't necessarily stop once you've ceased your employment.
Stopping him from working might be next to impossible, but if he were in fact caught somehow using Melbourne's intellectual property or knowledge for commercial gain with his new employer, it's a very different scenario and then he could very likely have an injunction put in place to stop him working and be personally sued by the Storm.
Again, this would likely have no impact on the Broncos as the agreement is between Donaghy and Melbourne, so he may be personally sued but it would be much harder for Melbourne to bring any sort of action against Brisbane even if they were able to successfully sue Donaghy, and again, they could only sue Donaghy if they could actually prove beyond a reasonable doubt that he had used their intellectual property after agreeing not to, which Donaghy would have to be incredibly stupid to get busted for in the first place.