And he exercises all the AUTHORITY of the first beast in his presence.

What we see here is the apparent swapping of roles. Remember the "spirit" nature of the sea beast (verse 1)?  Here the earth beast receives all the spiritual qualities of the first beast.

Furthermore, things of this earth are usually tied to money. Watchman Nee points out that "the son of perdition" is used twice in the New Testament. In John 17:12, "the son of perdition" refers to Judas Iscariot, one of the twelve disciples and also the money manager for the group. The second reference in 2 Thessalonians 2:3 points at the antichrist. Thus an argument can be made that the economic and religious systems of the world will combine to totally overwhelm all peoples of the earth except for those whose names are in 'the book' (verse 8).

Note also that this pair may be the devil's way to counterfeit the two witnesses (Revelation 11:3).

And he makes the earth and those who dwell in it to WORSHIP the first beast, whose fatal wound was healed.

The lure of wealth will cause many people to lose their faith (1 Timothy 6:10). Or rather, the fear of losing their earthly means of accumulating wealth may cause people to take the mark (verse 16). Either the lure or fear will cause the WORSHIPPING of the beasts to occur.

Much has been written about the "fatal wound". It is not clear when or how....perhaps it occurred in the war in the heavenlies (Revelation 12:7-9).  If this is true, we, humans, probably wouldn't recognize the "fatal wound" because it is spiritual in nature (Revelation 21:8).