They both have ultimates that cannot even be used without an ally. That inherently causes them to rely on at least one teammate to make use of their kit. No matter where they are played, I think they should be classified Support on the info page and under the collection menu, primarily so new players know that are at least in part a support class character and should expect it upon purchase.
EDIT: I think people are missing the point here? Under the new collection tab, it sorts by Role. This role is not synonymous with the lane where the champion is played. There, the Support role is composed of many champions with abilities that can heal, shield, augment, or otherwise affect one or more allies. There are champions there that are not played in the support role - like Orianna. Orianna has this "Role" in addition to mage because she can place her ball on allies and use abilities from their location. Shen and Galio both have game altering spells that can only be used on ally champions, so a large part of their kit is tied to "Support"