There is no doubt that two dialects of a language can be spoken in the same area, i have seen it in the same village. But there is a problem with your question. If two "dialects" are so different that the speakers of one could not understand the other, then generally they would be considered two different languages, not dialects, at least from a linguist's standpoint. However political/cultural/historical factors sometimes take over and things are called dialects that a linguist would call different languages.
So what we are talking about, from a linguist's perspective, is really two related languages. They are related enough and have enough cognates that the speakers of L1 can understand L2, and speakers of L2 can catch a few bits here and there but cannot understand L1. This is not only possible, but actual fact.
Consider Latin and Italian. If my understanding is right, Latin is the official language of the Vatican, but that just means that this language is reserved for especially important or official business, while Italian is often spoken throughout the Vatican and of course Italy. Your average Italian will not understand Latin, but because the two languages are strongly related to each other, he can catch bits here and there. Your average high ranking church official in the Vatican will speak both Latin and Italian fluently and be able to read and write both. Not exactly royalty and commoners, but a useful parallel.
Also take Koine Greek and modern Greek. The more educated a person is in modern day Greece, the more they will understand Koine Greek (ancient Greek, used in the New Testament), especially if they have any knowledge of classical Greek. But an uneducated Greek of today would gets bits from a person speaking or reading Koine Greek, but would get easily lost. And today there are people who learn Koine Greek (myself included), and can read it and understand it, but cannot understand modern Greek. There are also people, I expect, in Greece who have learned enough Koine Greek to be able to speak it fluently and read and write it (probably in the analysis and discussion of ancient documents, including the NT) and who are also fluent in modern Greek.
I hope you see the pattern - education. It would be easy to conceive a world in which only the nobility are educated. Because it is a medieval world, documents are not publicly available, and books and libraries are rare and only maintained by the wealthy nobles. Because there is no printing press, the language shifts - like happened to Greek and to English. Try to read John Wycliffe's translation of the Bible and you will not be able to understand it (Middle English) but read the Tyndale Bible (translation done just after the printing press - modern English) and you will have no problem. But in this world, the nobility decides that their education must all be carried out int the ancient form of their language, the one used for their most sacred documents, perhaps the very documents that established them as nobility. A noble must be able to read and understand their letters of patent, and all official business is conducted in the language of those patents of nobility. The uneducated commoner is lost. He catches a word here and there, but not more. The educated noble understands every word.