It looks like they do.
Maybe there is a new movement of people who like to call themselves Karaites. They can make up any believe system they want. Karaites, who still exist and have a small community in Israel and there are some from Egypt, are called Karaites, not Jews. Is there some reason why you WANT to believe they are actually Jews? Does this serve some purpose for you? You aren't Jewish, and you don't understand Jewish law, so how do you offer yourself up as an expert on the definition of Judaism? According to your logic, Jews are actually Christians, even if they don't believe in Christianity, because they have a similar foundation in the Torah (five books of Moses.) Frankly, I don't get why this is even being debated. Judaism dismissed the practice of Karaitism as not being Judaism a long time ago. As we have seen, even today, there are people who call themselves Jews who are actually not Jewish. If you would like to insist that Karaites are Jews, that is your deal. If you would like to find some Jews on FR who would like to join you in your belief, please go ahead. To say that you are still practicing Judaism if you don't accept Oral Law is nonsense.