>But... dark matter also doesn't interact with normal matter, so how would it create friction?

Dark matter interacts via gravity. Dynamical friction is a byproduct of gravity. When you have a large massive body inside a sea of much smaller particles, the large body's gravity changes the orbits of the particles near it in a way that creates an overdensity of small particles behind the large object. That overdensity creates a gravitational pull from those particles, in the direction opposite to the body's motion. Therefore, it behaves similar to a friction force.

Dynamical friction happens in any N-body system with a sea of "small" particles and some large particles. For example, it is the reason why supermassive black holes have to always be at the center of their galaxy. Dynamical friction with the stars would bring them in.