I was asked to design a 404 page but do we actually need to say 404? Even though most people understand what 404 means, do we need to explicitly tell users its a 404?
Why cant it just be an error page?
examples like these are really cool error pages. But they can get away without having the 404 in there. The context made it clear already. Why do websites still have it? When is it ok to break this rule?
Unfortunately, the 404 page is the only way of diagnosing a missing page (either because the page is missing or because the preceding link is broken) and forms part of a whole system of error pages that a server can produce.
For this reason, you still need to show "404" so that an engineer can distinguish it from the myriad other errors (my personal favourite is "418") that could be showing and could all have "user friendly" designs and messages. Without showing this number the engineer may not be able to identify the root cause of the problem.
By all means make it a less important part of your design visually but make sure it's findable for the engineers.
I had little argument with coder friends about 404. They said like this-"
You, designers, sometimes goes so wild,creative and funny, it is not easy for us to quickly figure out what page it is. So i ended up like this. 
It can be just an error page. I believe it is even better. It gives you more options to design something that is more suited for your users. 404 is a (mainstream) tech term. Not everybody knows what it means.
Create a better page where you specify what's wrong and what the user's next step can be (return to home, register, etc).
But they can get away without having the 404 in there.
As already noted in a comment: No, they cannot. Both of your examples mention 404 one way or another.
The context made it clear already.
Does it? At least in the Star Wars example, if I got to the error page from a search form, it would not be clear to me that there seems to be an actual error on the page (that tech support might fix if I contacted them), rather than this being just a case of my search yielding no results. (Well, it would be clear to me, because there is a big 404 there and I know what that means.)
Why do websites still have it?
You have to consider the different stakeholders for whom usability has to be optimized here. Maybe surprisingly, I see three groups:
Therefore, my conclusion is: Yes, it is needed, but it should not be the only thing displayed on such a page.
1: Don't get me wrong, they have every right to understand what is going on if they are interested in it. But if they do not care beyond the mere fact that there is an error, this is totally fine.
2: This can be especially problematic if the original message displayed by the website is already misleading or ambiguous. For instance, another answer here suggests the text "The page you are looking for is not under our radar." Now, to be "under someone's radar" is derived from the working principle of some kinds of radar that might not detect certain objects close to the ground, which can thus go unnoticed. Accordingly, the term is sometimes used figuratively to express that something remains unnoticed, invisible. The page not being under the website's radar might thus be paraphrased as "The page was successfully found.", which will totally confuse tech support staff.
So many answers and no actual answer. The purpose of 404 code is the indication of a missing page. Otherwise your "not found page" is 200 OK.
Without 404 the page is there, but, for example, there aren't any results to your search query, or the page is undergoing maintenance.
As simple as that.
p.s. Don't forget to tell search engines not to index your 404 page.
