Before I begin, let me mention that I am speaking about the mathematical world(one of the fields in which this paper was written). The following comments may not apply to other fields as I have no expertise. First of all, as the other reply mentions, no in fact they are not peer reviewed. That being said, arXiv is a preprint server and thus the content is fairly respectable. Additionally, this paper is by two authors at MIT the third at Bristol (fairly respectable schools).
Second, in the modern mathematical community, an enormous amount of important papers are not published. This is not a result of dumb reviewers, in fact most journals have a system for preventing this sort of issue. Their system is simple, most papers are reviewed by two people, each an expert in the field. I cannot argue that sometimes the paper will be beyond the scope of the reviewer, but with the connectedness of the mathematical community at present day, it is highly unlikely. The reason many papers go unpublished now, is because of arXiv and other preprint servers. Older faculty members have no need to boost their publication count so the actual publication is unnecessary. Additionally, most papers are only readable by a small subset of the mathematical community, and they are contacted directly. Also, nearly all mathematicians at this point are familiar with arXiv and use it as their main source of current research, thus reducing the need of publication. Third,
Also, I have read in my life thousands of published peer-reviewed articles
I am calling bullshit on this. I am currently in graduate school at a major university. There are several world famous professors here and one in particular is known for his ability to sift through papers extremely quickly. He doesn't read them, just skims to get the basic idea. He only gets through a paper a week maybe two. Assuming you are more consistent than him, and read two per week. And being more generous you blaze through 100 a year. You would be working at this pace for 20 years. While not impossible, highly unlikely. Especially since you mentioned that you "read" them not skim, and furthermore you are able to check them for trivialities, which takes considerable more time considering that you would have to evaluate the status of the paper.
A list is only as strong as its weakest link. -- Don Knuth