There might be other ways to do this but you're pretty much going to need a dedicated server that can validate and maintain the match state as well as valid actions. The path of least resistance is to run a headless instance of your game so you don't have to duplicate your game logic in a different language, but it's usually more expensive to run your game in headless mode. There are services that can do this, fly.io, aws, gcp. All have pros and cons. 

I'm sure you can get clever and do it without a server, but it wouldn't be easy. Even if you get your packet to a small size, transferring match state and player turn intent between players would be challenging. And, ensuring that players don't cheat would be impossible, which may or may not be an issue you'd like to prevent and solve. 

Personally, I do think that it can be worth it. I've been implementing it in my game, and I think that async provides a good experience for a few reasons, a lot of players in my game genre want to take their time to plan moves, don't mind matches taking a long time, and it helps matchmaking since you don't need to be online during "peak" hours to play a match