To me those flames are not an "engine Fire" as in the engine is on fire due to mechanical problems but rather some sort of compressor stall that occurred for some reason (bird strike could be a cause) and perhaps sorted itself out shortly after it began.
Interesting pictures none the less. You can see the right engine seems to be producing darker and more engine exhaust smoke prior and after the event although it could be because it was dark (low ambient light) when the pictures were taken.
Now why the crew decided to continue on an overseas trip is not for me to judge because we have no specific information on what actually happened.