Why pick 262144 Hz oscillator frequency?
As already commented, the accuracy doesn't depend on frequency.
It does significantly depend on temperature.


  What Is ‘High Accuracy Quartz’?
  Most watches rocking a quartz movement are guaranteed accurate to around 15 seconds a month or so. This is still much better than even the best mechanical watches, but there’s a breed of quartz watches out there that can do even better: the High Accuracy Quartz (HAQ). HAQ’s still operate under the same principals as standard quartz movements, but they take into account the one major threat to quartz accuracy: changes in temperature. HAQ’s are, thus, thermo-compensated and can detect these changes and adjust themselves accordingly, which typically results in a guaranteed accuracy rate of around 10 seconds per year.


Source: https://gearpatrol.com/2018/08/20/your-complete-guide-to-quartz-watches/

It's quite likely they used thermo-compensation, which has nothing to do with frequency.

A drawback of a higher frequency is a higher power consumption.
Their manual suggests the battery should be replaced each year which sounds frequent to me (I havent replaced the battery of my cheap watch the last 3 years).