Air carrier Captain reported a flaps failure on final approach and continued to land when procedures required a missed approach and new landing numbers.

Narrative

We operated from ZZZ1 to ZZZZ. The descent into ZZZZ was uneventful. The FO was PF and I was PM. The FO had called for flaps 1 and then flaps 5 as we prepared for the turn inbound on final. The FO called for flaps 10. At the same time we got a FLAPS DRIVE EICAS message. The FO called for the FLAPS DRIVE checklist. The FO in the observers seat asked if we wanted to break off the approach to run the checklist. I responded that I thought the checklist was short and no real change to procedures with it. I think I said if it looks long we would break off. I ran the checklist and found I was correct. The checklist does not take long to run. We adjusted the ref speed for the approach and continued. I asked everyone if they were okay with what we had done. Everyone answered yes. The FO in the observes seat said he had read through the checklist again and all was done. I elected not to request priority with ZZZZ Tower. As I thought about it later I probably should have. I did inform them that we would be coming in at a faster than normal approach speed. I told them approach speed would be 183 knots. The other thing I failed to do was have landing numbers run for the flaps drive failure. I completely forgot that the landing performance page had the non-normals section. No one else mentioned it either. I was surprised looking at the checklist later that there is no mention of recalculating the landing numbers. I think this would be appropriate in the QRH (Quick Reference Handbook). We were landing on Runway XXR in ZZZZ which is a long runway. I was not worried about having enough braking performance. The FO flying did a great job of touching down and going into full reverse. We stopped well prior to the end of the runway and turned off where we normally would have. We taxied to the gate with no further problems. As I said before; looking back I should have request priority and probably should have broken off the approach to checklist. My main hesitation was because we were in [foreign] airspace and the language barrier can be a problem there. The controller we had that night spoke very poor English. Probably the worst I have heard. But I should not have let that influence my decision as much as it did. Also; I believe the QRH checklist should have a statement about recalculating the performance. It is easy to overlook since you already have performance and the landing speed is not much greater.