That definition sounds reasonable, but doesn't cover the whole picture. So yes, sure, part of feminism is believing that women should have the same right to vote, to go to university, to be admitted to the same occupations as men, to have the same pay as men do.
But it ignores other important elements of feminism - the fact that women get pregnant and give birth, and may need extra protections, such as maternity leave, or guarantees of financial security because they often give up work to bring up children and become dependent on a male wage-earner.
Also the fact that women are open to sexual exploitation by men through prostitution and rape, and are often on the receiving end of male violence from family members, husbands and strangers. That is a massive issue that isn't covered by the words "have the same rights and opportunities as men". Look at the grooming gangs scandal: thousands of young girls subjected to horrific rape, torture and sometimes even murder by adult men, yet often not believed, and often prosecuted themselves for prostitution offences.
The biggest challenge for feminism is freeing women from male violence.