I believe the problem is assuming you release the object from rest (or at least constant velocity) and the only forces on it are gravity, friction, and normal force. You are not applying another force to it at the beginning by hitting the ball. If you did the physics would change. Their equations seem correct.

The angular velocity is a function of time $t$ so it's changing over time. It is not constant. The angular acceleration $\frac{5g}{2r} \mu_k$ is what's constant. This makes sense cause you would expect a constant torque (in this case caused by the friction force) to give a constant angular acceleration.

I believe the problem is assuming you release the object from a constant initial velocity $v_0$ and the only forces acting on it are gravity, friction, and normal force. You are not applying an initial force $F_0$ or initial torque $\tau_0$ to the ball at the beginning by hitting it. If you did the physics would change.

The angular velocity $\omega$ is a function of time $t$ so it's changing over time. It is not constant. The angular acceleration $ \alpha = \frac{5g}{2r} \mu_k$ is what's constant. This makes sense cause you would expect a constant torque (in this case caused by the friction force $f$) to give a constant angular acceleration.