To me, the concept of fairness seems worthless. In what sense are two people comparable? All people are different. If I am to make a choice, how can I determine what is the fair choice? What factors do I admit in this decision?
For example: suppose I have to choose whether to give a job to candidate A or B. Candidate A is white and poor. Candidate B is black and already has an offer. Candidate B is slightly more qualified for the position that candidate A. I could offer the job to B because he is more qualified, and that is arguably fair. I could offer the job to candidate A because he needs it more, and that is arguably fair. I could offer the job to candidate B because black people have been oppressed, and deserve affirmative action, and that is arguably fair. I don't actually agree with any of these arguments; I am pointing out that there are more choices about how to define "fairness" than there are actual choices, and that any particular definition of fairness contradicts the others. Ultimately, I have to make a choice about whom to hire, and the concept of fairness seems to only confuse the issue.
Let's suppose I offer the job to candidate A. I believe I have made that decision on the grounds that poor people have been oppressed by the wealthy and deserve affirmative action. Candidate B tells me that I have been unfair since I offered the job to a less qualified individual. How can I (or anyone else) decide whether my fairness is the correct fairness? Isn't fairness just a euphemism for power? Can candidate B control my decision by convincing me that it was unfair? Why should candidate B (or even society at large) make that decision? Am I not the person who has been charged to make the hire? Shouldn't I pick the candidate who is the best fit for the position, employing all the resources of my holistic intuition instead of blindly following a general prescription made in ignorance of the particulars?
In my analysis, depriving anyone of the opportunity to make a choice is a greater moral failing than an unfair choice. People need to make choices so that they can experience making good choices and bad choices. Only choices can have moral value, while following rules and orders is always amoral (without any moral quality). The right to make bad choices is more important than fairness.
Just to add one more example, let's apply this reasoning to OP's original example. The rules of the competition were clear. OP missed the deadline. Would it be fair to break the rules? Would it be fair to the other contestants who conservatively submitted their entries early to avoid any chance of missing the deadline? Would it be fair to ignore a clearly superior entry for the sake of following rules? Would it be fair to ignore a superior entry which took advantage of time that none of the other contestants who successfully submitted entries had available to them? Would it be fair to ignore an entry purely because of the possibility that the contestant could have worked on it after the deadline (the only way to be sure is to receive the submission before the deadline)? If the processing of the entries was automated, would it be fair to ignore an entry purely because it would be unfair to those running the contest to have to go to more trouble for a contestant?
In my opinion, all of these questions could be argued either way. Fairness only complicates the choice, which is whether to accept the submission or not. In my opinion, that choice belongs purely to the organizer. He should make the choice based on his aesthetic choice. Which would make a better contest (or a better world), one where he accepts the submission, or one where he rejects it? The contestant claiming that fairness requires the submission to be accepted is at best noise, and at worst harmful misdirection from the truth, which is that the choice is clearly in the hands of the organizer. The contestant has plenty of choices: whether to enter the contest at all, whether to complain about the server error, whether to accept the decision of the organizer peacefully, whether to enter future contests by the same organizer. All of his choices should be made in the same way, and fairness plays no part in any of it.
