Because of the ownership, there's not really a play area, per se. All the widgets for drawing cards and playing cards are within the pop-in windows. Cards that get 'played' go into a different state, like an ethereal discard, where they can be reshuffled back into the deck later on. When a card is drawn, ownership has to transfer to the drawer, otherwise anyone can see the card. The deck is usable by everyone (partial ownership), which means every card is owned by everyone. For simplicity, let's say your playing cribbage. The reason for this comes down to ownership. However, the interface isn't exactly what you think, as it's all done via pop-in windows. Foundry already has a built-in Cards system ( ) that allows each player to have their own hand, and a deck that they can draw from.
I'll preface this with: I have only worked with this for version 9. Quick Links - especially useful for new users! Welcome to /r/FoundryVTT - the community made and operated subreddit for the Virtual Tabletop software Foundry! Make sure to check out the Rules page.