How can you calculate battery run time?
The author has done three things: 


Remove the power consuming Power Indicator LED
Avoid using an inefficient linear regulator
Keep the micro in sleep mode as much as possible through software design.


He states that the 9v battery has a capacity of 1200mAh. This means that it can supply 1200mA for one hour or say 120mA for ten hours. 

If the circuit is ising 0.054mA then it would be able to run for 22222 hours (1200 divided by 0.54) which is about 2.5 years.