Everyman is meant to be an allegory for the battle between virtue and sin within the human soul. This idea applies to any human being, regardless of social class. Both kings and peasants would be able to understand the experiences of temptation and redemption.
Everyman was written as a product of medieval Christian culture, so one might justly question how universal all of its themes are to all "people living on Earth." It presents the Christian religion (in particular, Christianity through the lens of the Roman Catholic Church, which reigned dominant in Europe during the middle ages) as the one path to salvation. However, most of the major world religions also stress the importance of good deeds, and this is certainly stressed as important in Everyman; so in that sense, the play can be relatable in general.