Looking through https://github.com/OpenRailwayMap/OpenRailwayMap-CartoCSS/blob/master/standard.mml and https://github.com/OpenRailwayMap/OpenRailwayMap-CartoCSS/blob/master/standard.mss I'm suspecting the combination of service=spur and usage=tourism is what's causing this spur to not show on OpenRailwayMap.

I've also noticed that the main rail line to Bo'ness is tagged as usage=branch. I'm wondering if usage=tourism would be more appropriate as it's a tourist railway rather than a railway branch from a mainline, though it used to be a branch from the mainline.