Horizontally. There are large rounded structures at the end to provide a large enough turning radius for the belts to loop around.
Thanks. Finally got my answer.
Sorry I mistated the scenario so badly at the beginning.
Yup. Think of the belts like the luggage carousel at your local airport. They are composed of interlocking segments, each of which can turn independently so they can turn-- you’d need it built that way because a cross-Continent system would have to go around mountains, rivers, canyons, etc.
I mean of course the concept is ridiculous… who would build such a thing? But it’s just there for the purpose of telling a story.
for a very specific purpose
Since this has been bumped, I have to say that story horrified me for various reasons when I read it long long ago. It seemed to me impossible that the entire roadworking union wouldn’t be taken out and shot, followed by everyone realizing what a ridiculous idea the whole thing was and switching to rockets or pneumatic tubes or something else obviously far safer. 
I think some biography I read said Heinlein switched from liberal to more conservative viewpoint from the influence of his second wife, Virginia(?). Although, if you read Coventry, he does make a cynical joke of pure libertarians.
If you grew up in the 60’s or 70’s when strikes were common, the story made perfect sense; although one wonders why they did not have a “management team” that could jump in and turn the power back on. IIRC (again, been 40 years or more) the union bosses had barricaded themselves in the control room and so it was more of a case of endangering lives than of walking off the job - significant escalation of offenses. Maybe shooting or prison time was in order. (I think the story mentions one poor fellow having a collision between the 95mph belt and the stopped 100mph one, so there were injuries or fatalities. )