Depends on your definition of feminism indeed.
Yes, but only in a trivial sense. The super extreme view is held be a small fraction of people who inhabit certain places on the internet and happen to be very noisy. If you attempt to use that definition outside of that group, or people aware of that group, you will essentially be using a private definition and will be misunderstood.
I'm taking the current "modern" feminists (third wave feminism) which you can see in action on Twitter (eg. the GamerGate instigators).
I don't see how the instigators---either the dude who posted that long screed or the people attacking Anita Asrkeesian---are feminists by any definition of the word.
more modern definitions leave the equality out of it.
No, not really. This is not to say you can't fine some wingnut somewhere who does so. The internet is a large place and you can find someone professing to belong to some cause to say almost anything. The fact that a small number of nutcases exist doesn't really say anything about the general cause. Mostly, equality is left out on in the rather peculiar fantasies of TheRedPill, AVFM and other such places.
A traditional feminist movement in modern eras would be primarily focused on countries around the world where women don't have the rights yet to run for president
No. You're saying what YOU think feminists ought to do. There's still plenty to do back home. There is also more wrong in the world than any one person can try to fix, and complaining that someone is concentrating on a cause they like, not some other cause you don't even like enough to do anything about is a cheap rhetorical trick. It's meaningless because it can be levelled at more or less anything, because there is always somewhere else worse in the world. Come to think of it, why are you wasting time arguing on the internet when there are people being tortured in North Korea? You should be spending your time helping them.
you could just be a part of it and not see the issue of what your group represents (eg. if your definition of feminism comes from AmiMojo
If you're going to claim AmiMojo is part of a hate group then have a massive . That says far, far more about your biases than about his IMO.