It only takes ones reading every four minutes, which probably pushes the duty cycle for the processor and sensor chips down enough to make the energy budget.
Assuming a slow 3 seconds for each cycle of "wake up, initialize sensor, take a reading, store it to flash, set timer, go to sleep", that's a duty cycle of 1.3% which is pretty nice.
I know, that's why I said "slow". :) I wanted to aim for a very "bad" estimate, just to make the point more clearly: the duty cycle is low for this system.
You can't typically write just 1 byte into flash - you have to write in pages of say 4KB.
And writing to flash is painfully slow.
So it's most efficient (current-wise) to store up 4KB worth of data in RAM and then write it all to flash in one fell swoop.
It's a tradeoff with data security, but I think it's a good tradeoff because only rarely will things go wrong, but the additional current burn is guaranteed and constant if you write every datapoint to flash.
Magnetic FRAM is making a comeback just to scratch some of these low-power itches. It's faster, uses less power, and has greater write endurance. TI even put it in one of their latest MSP430's.
The large chip on the image seems to have a number starting with 16F (or maybe 18F), so it seems to be some PIC microcontroler in a 20QFN package. The other two black objects on the board seem to be the accelerometer and light sensor, there are loads of these available in these sizes from your favorite parts suppliers.
Assuming a slow 3 seconds for each cycle of "wake up, initialize sensor, take a reading, store it to flash, set timer, go to sleep", that's a duty cycle of 1.3% which is pretty nice.