This sounds to me like something the pitch man for a sleazy informercial might say!
I think, like the French's 'voudrais' and 'veux' what we are dealing with is parts of the same verb. In Italian the root form is 'volere' But if you want to use it for 'wish' which is closer to 'would like' you would use the conditional conjugation of the verb, io vorrei diventare ricco - I would like/wish to become rich. Or in the form here Vorresti diventare ricco - Would you like to become rich?
So because there is an Italian word that is closer to 'wish' then keep that translation for when that word is there.
Soglio is also right in that 'Do you wish to become rich' does feel a bit archaic.
Exactly. In any case, "vuoi" means "you want" (from the infinitive "volere"). To wish, desiderare, is a totally different verb.