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'.
In more modern times, many RTS games are asymmetrical: think SC2, Dota etc..
If you're thinking about board games, in particular, there's games like Terra Mystica or most miniature games that are designed with a vast number of factions that have differing goals.
Asymmetrical games are in fact hugely popular because they let people roleplay strategies that they may think are more fun