Technically, it is a ride for an Airman Certificate (CFI tickets are Airman Certificates), but not a practical test for a pilot certificate/rating. The actual words in 14 CFR 61.56 are:
Note the phrase "pilot proficiency check," not "practical test." The policy previously espoused by the Flight Standards Service in the no-longer-official Part 61 FAQ file was that since you have to "perform the procedures and maneuvers included in the standards to the COMMERCIAL PILOT skill level" on the CFI practical test, that constituded a "pilot proficiency check conducted by an examiner," and thus the successful completion of a CFI practical test met the requirement of 14 CFR 61.56(d). However, the Flight Standards Service also suggested (that's "should," not "shall") that the applicant obtain a logbook flight review endorsement as well as a Temporary Airman Certificate from the examiner just to make sure.
That said, to my knowledge, the FAA Chief Counsel has never officially ruled on the issue, leaving the matter legally uncertain, although perhaps the Baltimore FSDO has recently obtained such a legal ruling. If so, I'd like to see it. In any event, I've never heard of a flight instructor who had no 61.56 square filler other than a CFI practical test within the previous 24 calendar months being busted for failing to meet the 61.56 requirement.