The idea does sound interesting, but I think there is quite a lot of work in front of you. Few small tips / suggestions to get you started:
1) Implement single-player mode ASAP. Even if the opponent 'AI' moves randomly or just does nothing. Not only will it allow curious potential players like me to see the game board instead of only waiting screen, it will also help with debugging, simplifying your run/test/fix cycle.
2) If you want to publish your github repo (which is a good idea IMHO), add direct link to it, and maybe take a moment to do a little cleanup, at least removing default Vue's readme files. I was confused for a second when trying to look at your source. Also, maybe add a license.
3) Consider view/model separation right from the start. It is ok to do a quick prototype like you did, but intertwined UI and game logic will quickly become a hindrance, especially for a multiplayer game.
Anyway, good luck with development!