The definition of "to be" as a linking verb which you cite ("to behave in a particular way") does not imply that the verbs "to be" and "to behave" can be used interchangeably.
The verb to be is "special" in English, as it is in most languages. To be is complemented (or modified) by an adjective, and not by an adverb, as is the case with most verbs, such as "to behave."
You might find the arguments on this page to be interesting: What is the difference between "correct" and "right"?
The consensus there seems to be that "correct" refers to things that are provable, or factual, while "right" refers to opinions, or preferences. In other words, "correct" is objective (meaning there is external validation) while "right" is subjective (meaning that it varies between individuals).
In most cases "correct" and "right" are interchangeable, since there is often no difference between objective and subjective. For example:
She gave the right answer, that Nairobi is the capital of Kenya
This is both objectively and subjectively correct, since it can be both proven by external sources, and also is generally considered factual by most people.
The phrase "right English" is subtly different from "correct English". It implies that the person strongly that there is a right way to say something in English, which therefore means that anything else is the wrong way.
In some cases this may be true, but in many others it's purely subjective opinion. The perception is that, while there are certain general rules, there is enough subjective variation in English language use that "right" and "wrong" are not as important as whether a particular instance of English is "correct" or "incorrect" -- that it follows certain established rules.
To get to the point: it is possible to say, "That is right English", but it sounds both awkward and pretentious. The more common expression would be, "That is correct English".
Best Answer
It's wrong. This is deliberate on the part of the game designers. Peons are not known for being highly educated or well-spoken.
However, babies sometimes speak this way before they learn the difference between objective pronouns (me) and subjective pronouns (I). For that reason, incorrect constructions like "me (verb)" or "me (adjective)" are associated with "baby talk."