If this guy didn't have a fire extinguisher in the house, or didn't know or couldn't remember where it was, or thought he could put out the fire with a few buckets of water (I doubt if he had a hose handy inside), and panicked, he may not have been able to make sure a fire in the fireplace was out, or even thought to close the damper. Of course, if the fire was already up into the chimney, closing the damper would've only contained the fire in the fireplace, but not the fire above it.
If the fire had reached any walls or ceiling, this guy would have had a really big problem. That is probably not the case, however.
Of course, if the fire was already up into the chimney, closing the damper would've only contained the fire in the fireplace, but not the fire above it.
Uh, the first unintentional part of the fire was in the chimney (it was preceded of course by an intentional fire in the fireplace). And closing the damper would extinguish that fire quickly(*) but left the one in the fireplace burning. If the chimney fire was extinguished before it spread, extinguishing the fire in the fireplace without making a mess would be the hard part, and even that should be doable without excessive damage to anything (some smoke damage would be inevitable, but probably nothing that couldn't be cleaned off or lived with).
(*) Fires can burn very well in narrow vertical tubes that are open at both ends, but not well at all if either end is closed. If the top end is plugged, the spent air will accumulate in the top of the tube and work its way down until there is not enough oxygen above the fuel source to support combustion. If the bottom end is plugged, the intensity of the fire will be limitted by the requirement that fresh air enter the tube from the top in the direction opposite the convection currents. If the tube is wide enough relative to its length it may be possible to establish an airflow pattern that supports combustion (e.g. burning a candle in a jar). If the tube is comparatively narrow, however, convection will be relatively ineffective.