Ah yes, they absolutely have to be undead zombies. We definitely do not have any real world examples of zombies that are infact not undead.
Zombie literally means risen dead. Parasitic control and virus driven dementia aren’t zombification.
You know what they call a zombie that isn’t dead? A sick person.
Alright man look, I’m not going to sit here and have an argument with someone who is being this pedantic.
Yes, traditionally a zombie is someone who is undead. Traditionally speaking, a zombie also doesn’t eat flesh. You can look this up in Haitian folklore.
That being said, what we refer to as a zombie is a humanoid who attacks other humans and eats flesh with little to no higher functioning, as in below any living animal. Traditionally speaking, the mind-altered state is part of what makes a zombie a zombie, not just the undead part.