>>Have I missed pulling that ring (or race) out from the pin, and, instead, installing that ring (or race) into the hub?
It looks like that, yes. But, it's difficult to say with all that grease in the way.
Was the old bearing badly damaged?
If the race has stck onto the stub axle, it should not be too difficult to remove. However, if the race has spun, it's entirely possible that it has welded itself to the stub axle.