Power is very much related to the wealth issue. (Ever heard the phrase "money is power" or "money talks"? That's where we're coming from here.) The power dynamic in this poem is very clearly delineated: one man has all the power, and everyone else has none. The way in which Trujillo came to power is less important than what he does with it – he uses it to assuage his own unhappiness by inflicting pain on others. The simple historical fact of Trujillo's existence, even if the poem doesn't go into it explicitly, is an example of a power dynamic gone horribly awry. He is a dictator, and he used his leadership to arbitrarily violent ends. The massacre depicted in "Parsley" is something that only someone with immense amounts of power could do. So, thematically, power is hugely relevant to the poem.
In the poem, the dictator is both powerful (in his control over the Haitians) but also powerless (in his grief over his mother).
"Parsley" is a monument to the arbitrary use of political power, to terrifying effect.