The description of play in the article corresponds most closely to (straight) carom billiards rather than a variety of pool (or even three-cushion billiards). A run of forty is creditable; runs of 100 or more aren't uncommon among good players. There's a billiard table just behind the foreground pool table in the photo of the Quadrangle Club.
“... Michelson would run ten or twelve billiards with a touch so delicate that the three balls could always be covered by a hat.”
Michelson was playing billiards on a table without pockets.
I agree that Michelson wasn’t playing 3-cushion because not even Willie Hoppe (best player of that era) had runs 10 or 12 on a daily basis.
Balkline was still popular as an amateur game in the 1920s, so Michelson could have been playing one of the balkline variants rather than straight rail.
