It's still vegetarian, just maybe not vegan.
A more general definition of a vegetarian food is food whose ingredients do not purposefully include any product that requires killing an animal to extract it.
Note that the homeopathic definition of vegetarian means that essentially no food is vegetarian, because basically all grains and vegetables include small fauna that are inadvertently incorporated into the ingredient during harvesting.
Edit: Most vegetarians you happen to know. I personally don't like the fluidity with which the term is used expressly because it leads to confusion. You want to eat meat, cool you do you, but don't make it harder to explain for people who choose to actually follow the definition by making it meaningless. It's like the term "green" when people guest started using it it had a definition that was understood, now it's meaningless. If someone is comfortable with meat intentionally being in their food for to preparation to the point that they don't mind if there's meat in their food, they probably consume far more meat products than they realize and I doubt that they are as vegetarian a they intend to be, which again is fine, I just dislike claiming to be something that, by definition, one isn't and trying to torture the definition to your preferences.
If you adopt a definition of vegetarian that excludes any product that has a microgram of animal meat in it, you rapidly run into the problem that there is literally no vegetarian food, because dead animals end up unintentionally incorporated into pretty much all products in the processing stage. There's not even vegetarian water, because (animal) rotifers are present in it.
I say this all as a vegetarian who avoids fish sauce and animal-based broths, meaning effectively large swaths of Japanese and Southeast Asian cuisines are effectively off limits to me. The attempt to one-up the majority of vegetarians by demanding convoluted purity rituals for the right to claim membership in the One True Vegetarianism doesn't help anyone.
As an example of this issue in action, if you're taking your company out for food, it's a huge mistake to go to a place that only offers meat-like stuff for vegetarians and vegans.
I work in vegan food industry (own company and invested in others) and the market research we've done has always been consistent here that most vegans enjoy eating plant meats (ie- beyond / hungry plannet / impossible / gardein etc). Granted that research has been mostly in Australia and Hong Kong which is where I focus on