Michael:

I assume that dimension is the rotor diameter. But wouldn't a change
in rotor diameter change where the caliper gets positioned, i.e. would
require a change to the caliper mounting eyelets?

Disc brake manufacturers sell adaptors for different rotor and mounting
sizes. These may even be included with the brakes when you buy them.

I'm spec'ing these brakes for a road bike; should I expect to need
more stopping power than a mountain bike for say long mountain
downhills?

Be mindful of the fork manufacturer's recommendation. The larger the
rotor, the larger the stresses exerted on the caliper mounts.
Suspension fork manufacturers such as Answer and Fox recommend against
rotors 165mm on their non-DH-specific forks for this reason.

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