Check if the system is linear
I believe there's either a mistake in the presentation or the presentation is using a different definition of linear.

For example, the system is linear in $x$ from a system perspective, but it's affine in $x[n]$ (and, therefore not linear) because of the $bx[n-3]$ offset.

On this site, we tend to go with the system definition rather than split hairs about linearity versus affine-ness.