I think not. The characterization of "transcendental deduction" that you quoted from the SEP seems to me too liberal. Kant's sense of "transcendental deduction" is more specific than that. For Kant it is a kind of proof of right, a proof of legitimacy.
The backdrop of Kant's deduction is David Hume's criticism of the concept of cause. Hume argued that the concept of cause, as it is traditionally conceived, is not derived from sense experience, and is therefore illusory and illegitimate. Kant agreed that the traditional concept of cause is not derived from sense experience, but insisted that it is nevertheless legitimately applied to sense experience. It is to prove this legitimacy that was the task of the transcendental deduction. In addition, Kant observed that Hume's criticism applied not only to the concept of cause, but to the larger set of basic concepts that are being applied to the objects of sense experience - the categories. So it became the task of the transcendental deduction to prove the right, the legitimacy of applying the categories to the objects of sense experience.
Among the many conceptions, which make up the very variegated web of human cognition, some are destined for pure use a priori, independent of all experience; and their title to be so employed always requires a deduction, inasmuch as, to justify such use of them, proofs from experience are not sufficient; but it is necessary to know how these conceptions can apply to objects without being derived from experience. I term, therefore, an examination of the manner in which conceptions can apply a priori to objects, the transcendental deduction of conceptions, and I distinguish it from the empirical deduction, which indicates the mode in which conception is obtained through experience and reflection thereon; consequently, does not concern itself with the right, but only with the fact of our obtaining conceptions in such and such a manner. (Critique of Pure Reason Transcendental Deduction §9) (emphasis mine)
I see no parallel issue of legitimacy surrounding the concepts of Special Relativity. Einstein did tweak with the concepts of time, speed, etc., but he was not applying non-empirical concepts to experience, in the way that Kant was adamant to do. So the term "transcendental deduction" does not fit, in this case.