It was never an international weekend, only a representative weekend, however instead of it being Australia v New Zealand, the Pacific Tests and Country v City it is now Origin and the Pacific Tests.
As already mentioned by a few others on here, there is absolutely nothing preventing NZ playing anyone else.
Honestly I'm glad the mid year ANZAC Test has been scrapped. In the 17 odd years it has been running, it has never been given the respect it deserves. At least at the end of the year it is allowed to be a showcase in its own right. It also means it is a more level playing field (there is a reason it took NZ so long to win a mid year test again) when Australia and NZ go head to head.
More competitive Internationals breeds more interest which generates more sponsorship, bigger events and hopefully allows international RL to get the respect it deserves.