"At the end of the round, retrieve the dice from the right of the top dice space and then move the two dice next to the lower dice space up to the right of the top dice space"
Does it mean take the two dice at the bottom, and put them up top?
Yes. But remove the dice from the upmost dice space first. Which is only possible from 2nd turn on because the dice from the lowermost dice space go up there for the first time at the end of turn 1.