The Six Kings Slam may be unique
now, but as I've mentioned before, it's very similar to the Pepsi Grand Slam, a four-man tournament in the late 1970s. It was played in January and brought together the slam winners from the just-completed season. The format was two semifinals, the final, and a third-place match. Although probably originally designed as a big-money exhibition for the top guys, it earned some legitimacy, and its results are included in the official ATP head-to-head stats. I'm not sure whether the matches generated Grand Prix or computer ranking points.
The Pepsi Grand Slam is a good example of why lumping all "exhibitions" together is an unsound practice. You can have players on the court wearing headsets as they tap the ball back and forth while insulting each other and raising money for tsunami victims. You can have players trying out trick shots on courts that are half one surface and half another. Or you can have a mini-tournament in which winners and losers are clearly identified, thus providing a real competitive incentive for most participants.
The Pepsi Grand Slam had a meaningful impact on tennis history, IMO. Bjorn Borg won his very first match against Jimmy Connors in 1973, when Borg was 17 and neither he nor Jimbo had yet displayed their ATG levels. But after that, Connors won six matches in row, including two huge matches at the U.S. Open (SF and F). Borg seemed a little intimidated. What turned the tide was the 1977 Pepsi Grand Slam. Borg defeated Connors in a close three-set final. It was reported that Borg said to Connors at the handshake, "I get you finally." After that match, Borg bested Jimbo 13-2 in their head-to-head. Even the
New York Times treated the match as serious, big-time tennis.
https://www.nytimes.com/1977/01/24/archives/borg-ends-dominance-by-connors.html.
All this doesn't prove that the Six Kings Slam is tennis history in the making, or that the result of the Sinner-Alcaraz final will exert a significant influence on their rivalry. But the possibility shouldn't be dismissed simply by applying the "exhibition" label.