Deriving the inverse kinematics of swerve is basically finding the module velocity vectors that correspond to the robot state, which consists of the robot’s translation velocity, and its angular velocity. Those module velocity vectors are found by calculating the vector sum of velocity vectors resulting from only translation and only rotation. In your question, the circled part concerns rotation.

To rotate the swerve, each module will have to drive in a direction perpendicular to the center–or else, there would be wheel scrub. The vector r could be denoted by (W/2, L/2). The vector perpendicular to it would then be (L/2, -W/2). Multiply this vector by the rotation magnitude, and you would get what is shown in Ether’s derivation.

IIRC, omega should also be a vector, pointing outside the page, and the multiplication is actually a cross product, which would yield a vector perpendicular to both of the given vectors according to the right hand rule