We need one more person to play cards.

Literal

Cards [object-を] do [purpose-のに] one-more person necessary [copula-だ].

のに has two distinct uses: (a) 'although' after full clauses, and (b) the purpose reading V-dictionary + のに = 'for the purpose of doing V.' This sentence uses (b). トランプ comes from English 'trump,' borrowed into Japanese and semantically broadened to mean 'playing cards' in general — a classic loanword semantic-shift case.