There is no change from Matthew 5:3. The form of the Beatitudes is to start with a declaration that a people who are usually considered distinctly not blessed, will receive a blessing in the heavens.
In this case, the poor on earth, where they have no power or kingdom, receive a kingdom in heaven. The intended contrast is between their poverty on earth, and heavenly wealth.
The idea that they are poor in spirit goes along with the idea of poverty. Alma specifically noted that correlation in The Book of Alma:
12 … Ye are despised of your brethren because of your exceeding poverty, that ye are brought to a lowliness of heart; for ye are necessarily brought to be humble.
13 And now, because ye are compelled to be humble blessed are ye; for a man sometimes, if he is compelled to be humble, seeketh repentance; and now surely, whosoever repenteth shall find mercy; and he that findeth mercy and endureth to the end the same shall be saved.
14 And now, as I said unto you, that because ye were compelled to be humble ye were blessed, do ye not suppose that they are more blessed who truly humble themselves because of the word? (Alma 32:12–14)