Asymmetrical Gameplay
What makes gameplay asymmetrical? This is a complex discussion because it relies on where you draw the border. Chess is an "asymmetrical" game because white starts before black. Its asymmetrical because the starting positions are different.
Other games are asymmetrical because their victory conditions are different. What is the objective and how it can be achieved is quickly different.
In general, we can say that gameplay is asymmetrical when there are noticeable differences between different gameplay of two players. A prime example is excluding one player from a feature.
Sometimes its done by saying the player cannot engage with other diplomatically, other times they say you cannot declare offensive wars. Here asymmetrical gameplay is created by reduction. We take something away.
Other times a player has a specific feature he only has. This creates asymmetrical gameplay by addition.
The stronger, the additions or reductions are, the stronger the asymmetry becomes. This is a key insight.
Why Even Bother?
Creating asymmetrical gameplay opens the gates for quite unique play styles. I really like Endless Legend 1. My favorite faction are the Cultists. As they can only have one city and cannot create more. But their capital city can grow bigger than all other cities. They increase their empire by influencing surrounding tribes and converting them. Basically they integrate the surrounding areas into their cult.
In the end you mostly rely on a mix of wildly different units because your armies will be composed out of the types of tribes you converted. This results in armies that are much more divers in composition and nature than other factions. This has It's up and downsides.