First, to quickly address your explicit question in boldface, here's the official words from Thomson Reuters regarding their journal selection process for Web of Science and annual review:
While they apparently take timeliness and peer review very seriously, my impression is that a single instance of slow external review is not a strong enough reason to remove a journal. As this recent blog post on Nature shows, they do ban journals rather aggressively when they feel necessary. But those dropped journals are serious offenders of abuse and are clearly hurting Thomson Reuters' business.
Every researcher experiences unfair rejection in some way or another once in a while. I understand that it is very unfortunate that this has happened at a very early stage of your career. But this seems to be a lost cause at this point. And if you are sure that it was unjustifiable and if you do want to take some action, the best you could do seems to be let Editor in Chief know exactly what happened by writing a letter from an objective viewpoint in polite language and in sober tone and ask them to consider what they might be able to do to improve contributor experience. If you do not receive a satisfactory reply from them, you might consider reporting everything to the publisher that owns the journal.
But before you take any action, you should ask opinions from experienced researchers in your fields, such as your advisor. This is very important because different fields have different cultures in academia.
I assume that you are enrolled in a Ph.D. program in mathematics; I saw your post on MathOverflow. If this is the case, you might want to take a look at the most recent yearly report by American Mathematical Society on how long it typically takes for a paper to get accepted:
As you can see, the median time from submission to final acceptance varies greatly from journal to journal. You might want to notice how it takes a long time to get your paper reviewed by some of the most respected mathematics journals. For instance, Annals of Mathematics, which is arguably the most prestigious journal in mathematics, takes 24 months on average for review. The Memoirs of American Mathematical Society averagely takes more than 18 months from submission to acceptance. Granted that the practice of these journals is more of an exception than the norm, two years of review is certainly not unheard of in mathematics. So, while I tend to believe that your paper could have been reviewed much more quickly because a typical paper certainly does not require two years, it is impossible for us to tell if it was unjust or not without more context.
As for the priority issue you brought up, if it is in mathematics, I must say that you should not be surprised if you do not receive much sympathy. Reading your post, it appears that you did not make your preprint available to other members of the mathematics community before or soon after submission. Because mathematics has a much longer review process than other fields, it is quite common and, I think, very important to disseminate your results as soon as possible by, for example, uploading your preprint on arXiv or directly sending it through email to people you are sure will be interested. In fact, some journals explicitly encourage authors to upload their preprints on arXiv upon submission.
With that said, I understand that arXiv and other means of "pre-publication" are not for everyone. In mathematics, for example, one Fields Medalist mentions unpopularity of arXiv among East Asian authors he noticed during his little experiment on arXiv usage. As someone who was born and raised in Japan and received a Ph.D. from a Japanese university, I know how people may have their own valid reasons not to make their preprint public. You may have some strong belief or policy regarding science publication models as well. I din not use arXiv when I was a graduate student in Japan, either. However, you should not complain when someone "beats you to it" when you could prevent it by following the normal practice in the community.
Now, if you managed to read this wall of text this much, that means that you are the good kind of person who can stay calm and be in control of yourself in a tough situation. And, obviously, you have good math skills with which you proved new theorems worth publishing. So, if there is one thing I am sure of, it is that you have been heading in the right direction as a graduate student.
If you feel like the journal caused an unnecessary delay or "gap year" of some sort to your career, I guess you're right. But personally I try not to overthink, and try to think it's just another unavoidable glitch that often gets us out of the blue in our lives. (Notice the word "try." I fail very often.) You know, there are so many horror stories like yours out there in mathematics... (And never ask why I've been doing a postdoc for so many years!) It sucks for sure. But probably the best you can do now is talk to your advisor, who is there to give you advice anyway, and get back to your math life as soon as possible to prove more theorems. Good luck!