Well, I wouldn't use the language "identified this as a square matrix by column matrix." Sakurai appears to have identified Eq. 1.3.25 as an application of the rule for multiplication of a column vector by a square matrix. The final result, as we can see, is a bracket (a scalar). To go from the first line of 1.3.25 to the second, all Sakurai did was insert the identity in the form of
That's certainly a square matrix.
I guess I'm not entirely sure what your question is. Perhaps my comments could help to clarify your question? Are you asking why Sakurai can write down Eq. 1.3.25? Or are you asking how he recognized 1.3.25 as, partly, the multiplication of a square matrix with a column vector? Or something else?