No this is what veganism is. Veganism goes back to the Vegan Society and it's fight for the rights of non-human animals. Many people claim to be vegan without actually being vegan and I will not be diluting the definition. Veganism is at it's core about animal rights. There are plenty of reasons to go with a plant-based diet. A plant-based diet is part of veganism, but they are very much not the same thing. If someone claims to be vegan but still goes to the zoo or buys pets they did not understand what veganism is.

Edit: here is the vegan societies definition

"Veganism is a philosophy and way of living which seeks to exclude—as far as is possible and practicable—all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of animals, humans and the environment. In dietary terms it denotes the practice of dispensing with all products derived wholly or partly from animals."

- https://www.vegansociety.com/go-vegan/definition-veganism