How many modern games are two-player asymmetrical? I only know of Android: Netrunner. I hope we can continue learning more concrete rules for the ancient version of this game. It would be nice to have its history understood like chess'.
Strictly speaking most modern (two-player) games are two-player asymmetrical, since one player has a first-mover advantage. Not what you meant of course, but worth considering; it's somewhat hard to make a game that's strictly symmetric.
Also, take any two-player game, and create a new game where the players play the original game twice, switching sides, and you end up with a symmetrical game.
If you play both games in parallel, where each player can choose in which source game to play on each turn, I think you still end up with a symmetrical game (in some sense)