I think that you'll find newer entrants to the field argue you don't need CSS (or HTML or Accessibility) knowledge. They will say that these are someone else's responsibilities.
My take is that if you are responsible for what is delivered to the client (the response) you are also responsible for all the aspects that the user interfaces with.
Otherwise the argument is that's there's a front end to the front end called the interface which is someone else's responsibility.
Some businesses may have designers that code components and CSS however I'd argue that that's still "the front end" and that if the designer "can't wire it up" then the job of front end engineering is shared by designer and developer, rather than split.
So, my answer would be "no", you're not a "complete" front end engineer if you don't know CSS, HTML (semantic/current version), accessibility and browser APIs.
You can be a front end engineer who is learning those things and needs help from others to deliver a "complete" front end, that's fine.