"Those who dwell on the earth" is a formulaic expression in the book of Revelation, and it simply means those who want nothing to do with God, the worldly. Maybe the easiest way to define it would be simply "the carnal," "the fleshly." Colossians 3:1-2 shows the opposite of this:
If then you were raised with Christ, seek those things which are above, where Christ is, sitting at the right hand of God. Set your mind on things above, not on things on the earth.
There is a definite distinction between those who are godly, who seek heavenly or godly things, and "those who dwell on the earth," who seek earthly things. The latter are those who have no higher spiritual desire in life. They are perfectly happy here with their lives on the earth. Anyone who wants to tell them about the truth of God just gets the cold shoulder. They have their minds set on things of the earth.
Revelation 11:10 contains a set of three verbs—"rejoice," "make merry," and "send" gifts. The sense is that these carnal people will be joyful and celebrate and make a holiday out of the news of the witnesses' deaths by sending gifts to each other. All of this action that they take grows out of a sense of relief that their problems have been solved now that the witnesses lay dead. "Happy days are here again," in other words.
They will be so happy that these witnesses, who have been thorns in their sides, have been defeated—been killed—that they will put on a wild celebration, maybe for the whole three days. They will be ecstatic that these men who tormented them (as they think of it) are finally removed from the scene and out of their hair. Now, their supposed "heaven on earth" can continue. But it is a false "heaven on earth"—it is actually the abyss on earth, but they do not realize it because they have been thoroughly deceived.
The word "tormented" is the same one found in Revelation 20:10:
The devil, who deceived them, was cast into the lake of fire and brimstone where the beast and the false prophet were. And they will be tormented day and night forever and ever.
Satan and his demons will indeed be tormented. What the Two Witnesses do to the people of the earth at that time will not be torment, but that is how it will feel to these carnal people. The strongest meaning of this word in Greek means "torture." On the other end of the word's spectrum of definitions, it can mean "vex," a kind of irritation. It can also mean "harass," "distress," or "question," as in the sense of "interrogate under duress."
Perhaps the most interesting of the definitions of this word is "test." The two prophets will test these carnal people, and they will fail miserably. They will think the tests are torture and stubbornly refuse to change. We can easily see this in their actions: They will rejoice at the witnesses' deaths.
Notice that the Two Witnesses are called "two prophets." They are not called apostles or ministers. They are called prophets specifically because that is the essence of their work. They do a prophetic type of work rather than an apostolic type of work. The two overlap at points, but God emphasizes the prophetic one here.