And they didn't use GPS - doesn't work under rock.
I assume they did a bunch of calculations and monitor the position of the cutting heads relative to the path they had cut.
It does curve quite a bit.
On my layout, I mark the track position first with a pencil on the baseboard. I then lay some cork roadbed, then I redraw the lines. I use a metre rule, keeping the centre of the track aligned with the line. If I need a parallel track, I use a Peco track-gauge which works quite well.
I assume they did a bunch of calculations and monitor the position of the cutting heads relative to the path they had cut.
It does curve quite a bit.

On my layout, I mark the track position first with a pencil on the baseboard. I then lay some cork roadbed, then I redraw the lines. I use a metre rule, keeping the centre of the track aligned with the line. If I need a parallel track, I use a Peco track-gauge which works quite well.