Originally, the switch completed the circuit to the filaments (no series cap). The two pins on the end were not shorted out. Beside heating the filaments helping to lower the ionizing voltage, the momentary contact and extra current flow would cause the inductor to kick back with a higher voltage to help to ionize the gas when switch was opened. You held button switch closed for a couple of seconds, seeing the ends of bulb glow, then it would start up when button was released. There are starters that do this function automatically with a momentary switch. Run level voltage is much lower then what it takes to start (strike) the bulb. That is what the ballast is for. It make the drive approximate a current source, not a voltage source.
It works because you are running from 220 vac mains. For U.S. 120 vac mains, this circuit would likely not work.
Anyway, if it ain't broke, don't fix it. Did not think many folks were still using UV eproms these days.