It is both. There is no continuous aspect in German, so both English forms are possible and accepted.
Wir essen = "we eat" and "we are eating"
Du trinkst = "you drink" and "you are drinking"
Ich schlafe = "I sleep" and "I am sleeping"
Die Frau spielt = "The woman plays" and "The woman is playing"
the formal translation for "eating" as present participle would be "essend", but you cannot say "wir sind essend"
you could say as hedi76 writes: wir sind am essen, but for me this would be rather familiar,
best translation to me seems: "wir sind dabei zu essen" (similiar to French "etre en train de")
I'm not quite sure what you mean.
Are you asking why Wir essen translates into "We are eating"?
English has a present continuous tense, formed with "to be" and the -ing form of a verb.
German does not have such a form. It just has one present tense, which it uses both for habitual actions (e..g wir essen = we eat) and for actions that are taking place right now (e.g. wir essen = we are eating).
For an action that takes place right now, you will have to translate the German present tense into the English present continuous tense. That means using the verb "to be" and the -ing form of a verb. This is something dictated by English grammar, and not something present in a German sentence.
You could add "gerade" (has about the same meaning as "just"): "Wir essen gerade" means we are [just in the process of] eating. Other related phrases are "Wir sind [gerade] beim Essen", "Wir sind [gerade] am Essen" or "Wir sind [gerade] dabei, zu essen", as Marie_goforit and hedi76 said above. Please note that the use is different from the English "we are eating". These phrases would only be used if you wish to stress the fact that something is happening right now (for example, if indicating to someone on the phone that his/her call is ill-timed).
The hints do not say "... is okay in this sentence"; they are not "suggestions" or "recommendations".
The hints may include translations that work in other sentences but not this one. They are not reliable.
"We are eating." is correct English, and "We eat." is also correct English. Both of those translations are accepted.
"We eating." is not correct English and is not accepted as a translation.
Is there any particular reason why Duo considers "We're eating" to have a typographical error?
Do you have a screenshot showing Duolingo marking "We're eating" as containing a typo? If so, please upload it to a website (e.g. imgur) and tell us the URL.
"We're eating" should be accepted, so unless we want to talk about hypotheticals, it would be helpful to see evidence.