How do I get the requirements in a module's composer.json merged into the consolidated composer.json?
I think I've figured it out.

This is supposed to happen automatically. If the module is enabled with drush under Drupal 7, it does.  If you use other means to enable, the module, this might not happen.

In case the root composer.json for some reason is missing 
the requirements for a specific module, using drush to disable and then again re-enable the module fixes the problem.  E.g.:

drush dis composer_manager -y
drush en composer_manager -y


This seems to be all that is required.

It should be emphasised that this is only valid for Drupal 7. Drupal 8 is a completely different beast.