It depends upon whether the players are on the same system or not, and the exact mechanism by which the moves are communicated to each other.
If they are on the same system, then that's likely a hotseat game:
Hotseat or hot seat is a multiplayer mode provided by some turn-based video games, which allows two or more players to play on the same device by taking turns playing the game. The term was first used as a reference to playing a PC game and trading seats with the other player, but the mode dates back to early 1980s arcade games.1 A notable example of games that use this mode is the Heroes of Might and Magic series, which allows up to 8 players to play locally on the same computer.
If they are communicated via email, then you could call it a play-by-mail game:
Play-by-mail games, or play-by-post games, are games, of any type, played through postal mail or email.
Play by mail games are often referred to as PBM games, and play by email is sometimes abbreviated PBeM—as opposed to face to face (FTF) or over the board (OTB) games which are played in person. Another variation on the name is Play-by-Internet (PBI) or Play-by-Web (PBW). In all of these examples, player instructions can be either executed by a human moderator, a computer program, or a combination of the two.
If they are communicated over the web, then that can be called play-by-web:
An increasingly popular format for play-by-email games is play-by-web. As with play-by-email games the players are notified by email when it becomes their turn, but they must then return to the game's website to continue playing what is essentially a browser-based game.
Increasingly, this format is being adopted by social and mobile games, often described using the term "asynchronous multiplayer".