That's the only thing you would be sending over the network. So for example, you might have a move that is 'Black Queen moves to square H2'. The multiplayer part of chess involves sending data about the moves the player made over the network to the other player (maybe with a server in between). Neither of these would affect the way you implement multiplayer at all. You could make chess either with 2d sprites or UI elements. That's what I mean by the presentation (how we draw the game on screen) is independent of the way we implement multiplayer (how we transmit information between the two players). You could send that same piece of data and draw the result of that on either a bunch of UI elements or on some 2d sprites. Notice that statement doesn't include any information about sprites, or UI elements.
I don't know anything about your game, but let's talk about chess as an example. Either of these has nothing to do with the multiplayer aspect of your game. Using UI is one way to present the game to the player.
