1080p is only slightly less than 2K (1080p is 1920x1080 and 2K is 2048x1080) and even now a vast majority of DIs (digital inter-positive) are done at 2K, so the movies are usually shot/scanned at 4K or more now, but all the post processing is still being done at 2K - even for films such as The Hobbit, which was shot 5K but the finished film simply doesn't exist at a resolution higher than 2K, because a vast majority of digital projectors in cinemas all over the world are 2K or less anyway. So in theory, 1080p is perfectly fine for cinemas. The 2004 master having a lot of other faults is another story of course.