"To play, one needs to draw a card."

Translation: Pour jouer, il faut tirer une carte.

[d10MplTj]

Why not "on a besoin de...."?

[fugrank]

Is pulling a card the only/normal way to say this?

[Ripcurlgirl]

Tirer is the common verb used to mean "draw", as in a card, a curtain, even a bow to shoot an arrow, yes.
See examples here:
http://www.larousse.fr/dictionnaires/anglais-francais/draw/576905 and
https://www.wordreference.com/fren/tirer

[5004cupcake]

It also means to shoot a gun.