In the movie "The Book of Eli", why did the writers not conjugate the verb in "Cursed be the ground for our sake"?

This is an archaic use of the subjunctive, which only survives in certain fixed phrases. Compare:

Long live the king.
God bless America.
Heaven forbid.
Devil take the hindmost.

It means "May the ground be cursed."

To answer your updated question, the subjunctive in English should probably be considered as a conjugation rather than a semantic construction—that is, "long live the queen" should be called a subjunctive, but the modern-day equivalent "may the queen live long" should not. The subjunctive conjugation in English was used for so many diverse meanings that it is difficult to say what meanings should be considered subjunctive. So I would call it not "an outmoded method of writing the subjunctive" but "an outmoded use of the subjunctive".

You are correct that the form be here is a somewhat archaic imperative—not truly a subjunctive, though identical in form. But your paraphrase misses the mark: the equivalent PDE (Present-Day English) form for this third-person imperative would be “Let/May the ground be cursed,” and not “It is necessary that the ground be cursed.” The latter paraphrase errs in attributing agency to an impersonal necessity rather than to the speaker’s own commanding will. (In the context of Genesis 3.17, of course, the speaker is Yahweh, whose will is conceived as sufficient to effect anything, and the archaic imperative is more suggestive of this power than the PDE version.)

In the clip you link, Eli is more or less appropriating the voice of Yahweh and his original malediction, but emphatically substituting our for your (or KJV thy), meaning that he and those around him are alike fallen humanity, sinful in nature. He could very well have substituted indicative is for be, but retains it for its archaic, Biblical, maledictive flavor.

The example you mention in comments, “I be studying,” is a different animal altogether: that is the habitual be of African-American Vernacular English. If those who use it are joking around, their joke consists in pretending to be, or making fun of, African-Americans. And if so, they might very well not understand that this construction has a distinctive iterative aspect in A.A.V.E.