If they call themselves Jews, why would they call themselves Karaites? Do you know any Karaites? The ones in Israel aren't considered Jews and would have to convert in order to be Jewish. So again, it really doesn't matter what a pamphlet or website says. THEY AREN'T JEWISH. Are you Jewish, ChicagoHebrew?
They call themselves Jews and Karaites, just as a Chabanik calls himself both a Jew and a Chabadnik, and a Sephardi calls himself both a Jew and a Sephardi. They don't see a contradiction. The State of Israel considers them Jews, and Karaites are eligible under the law of return, but they are listed as Karaites on their ID cards. Orthodox rabbinic Jews don't obviously consider Karaites Jewish (although that requires a tortured interpretation of Jewish law, given that Karaites descend from clearly identifiable Israelite populations), but that doesn't mean Karaites don't consider themselves Jewish. You might be thinking of Samaritans, who forcefully deny that they are Jewish.
Yes, I am Jewish, and not a Karaite. Although I sympathize somewhat with Karaites on certain issues.