IMO:
Mark of the "beast" (a.k.a. "antichrist") is a physical mark/object on the hand or forehead (Revelation 13:16-18). My impression is that it is a chip, like the chip on a credit card. Without the chip it will be difficult to buy necessities. Revelation 13:12 says "την γην και τους εν αυτη" ("the land and those in it") referring to the Middle East. There was no concept of planet earth in biblical times.
I don't know what the mark of the beast is but IMO you are correct about the meaning of Revelation 13:12's "the earth" - wherever that "the land" is (I don't know where it is).
1 Samuel 2:8
He raiseth up the poor out of the dust, and lifteth up the beggar from the dunghill, to set them among princes, and to make them inherit the throne of glory: for the pillars of
the earth [erets] are the LORD'S, and he hath set
the world [tebel] upon them.
1 Chronicles 16:30
Tremble before him, all
the earth [erets]! The
world [tebel] is established, it cannot be moved.
The Hebrew uses word [erets] for "land" (not the planet earth, but the land)
throughout the flood narrative:
Genesis 6:12
12 And God looked upon the earth [erets] (the land), and, behold, it was corrupt; for all flesh had corrupted his way upon the earth [erets] (the land).
13 And God said unto Noah, The end of all flesh is come before me; for the earth [erets] (the land) is filled with violence through them; and, behold, I will destroy them with the earth [erets] (the land).
"And I will establish my covenant with you; neither shall all flesh be cut off any more by the waters of a flood; neither shall there any more be a flood to destroy the earth [erets] (the land)."
2 Peter 3:5-7
For this they willingly are ignorant of, that by the word of God
the heavens (ouranós) were of old, and
the earth [gē] standing out of the water and in the water: Whereby
the world (o kósmos) that then was, being overflowed with water, perished."
The word Kosmos in the Greek = "world" - it does not mean "universe" or "Cosmos" ("the heavens") (as it does in English).
Matthew 2:6
And thou Bethlehem,
in the land [ge] of Judah, art not the least among the princes of Judah: for out of thee shall come a Governor, that shall rule my people Israel.
So yes, the word ge is talking about the land, not the whole world - wherever that "the land" is (I don't know where it is).
There is also this difference between a beast rising from 'the sea' and a beast rising from 'the earth' (Revelation 13:11)- again the word is ge. Out of what land do you believe that beast will rise?