Well the watch doesn't keep them on all the time, and they've only used two.
What is the actual power consumption of nixie's? I've seen they run at around 170V and draw ~4mA. That's 680mW. With an 80% efficient driver that's 260mA @ 3.3V. On a 300mA battery that wouldn't last long, a bit over an hour to power one. Perhaps with some PWM and again, only turning them on intermittently you could extend that quite a lot.
If you have an interest in nixie's I recently watched a mesmerizing video about a guy who's started making them https://www.youtube.com/watch?v=wxL4ElboiuA
I know devfirat has made some clocks using some old nixie's but I don't know if he ever did a watch?