It was not only because of the familiar stance and fighting style, but also because of Hazel's brutality.
River could be stealthy when she executed her mission. However, an assassination was not always a clean job. At times, it could get messy, and River would show her brutal side.
She attacked not to make a quick kill, but to destroy her opponent. Instilled fear in the process. Inflicted more injuries than necessary until her opponent died from them. Battered and almost unrecognizable.
This was River's method, and Arlo knew this by heart. Before they were lovers, they were childhood friends. He grew up with her. He remembered her quirk and habit.
Therefore, it seemed as if River was there to take revenge on him when he saw Hazel attacking him with brute force.
