As I recall, the gap is very long, and the spark propagates along the gap. The laser beam is parallel to and within the gap, where the abruptly ionized nitrogen may be found.
A friend and I discussed building this gadget, but never did.
Now that I think about it, the dielectric might have been glass, versus G10.
Joe Gwinn
PS: As for Vannevar Bush and John Early Jackson improving the Shortt Clock, the article was in the 1 July 1960 issue of Scientific American. It cost only $8 to buy a downloadable copy of the whole issue, so I went for it. I recall reading this when it first came out, but didn't completely understand it then. JMG