How does peer-review work for "gigantic" collaboration projects? Big collaboration projects such as LHC experiments  (ATLAS, ALICE _e.g.) and LIGO result in academic papers featuring hundreds or even more than 1000 authors. Correct me if I’m wrong, but in fields like particle physics, researchers seem to belong to one of a small number of possibly competing collaboration projects. So if a paper resulting from a huge collaboration is submitted for peer review, the number of qualified referees would be very small (excluding researchers from competing collaboration projects), such that the anonymity of the referees would likely be compromised.

Is peer review still meaningful for papers resulted from huge collaboration? If yes, how should it be conducted?
While I am not certain about physics, I can speak for biology, which also has a large number of mega-author papers.  There, the overall field is large enough and well enough connected that, although a massive number of biologists may have a conflict of interest, an even more massive number of biologists are not directly involved but still working in areas close enough to be good reviewers.

I also have a suspicion (though I cannot back this up with data) that mega-author papers may in general have an easier time in review than typical small-collaboration papers.  Peer review evaluates papers along several different axes,
key among which are presentation quality, significance of problem, validity of experimental method, and interpretation of results.  

In the case of a massive collaboration, typically the questions of significance and validity of experimental method are long resolved: by the time the human genome was submitted for review, nobody was questioning its sequencing methods and a large scientific community was just waiting for enough data to accumulate; likewise for high-energy particle physics experiments.  Similarly, no mega-author paper should be able to be submitted without enough eyes on it to ensure that the presentation is decent.  That leaves interpretation of the results, and my understanding is that these mega-author papers tend to more focus on presenting data (which is already known to be of interest) rather than on its interpretation, and the interpretation (e.g., "What can we learn from the human genome?") is sorted out across many later publications.

Thus, review of a mega-author paper may actually be much easier than a small paper, simply by virtue of the difference in its goals and scale.