On first contact with the tower he called established ILS 06 and was told wind 300/11 kts so basically fully cross. He was then cleared to land and given a wind 270/25 knots which he seems to have missed. I have known tower controllers prompt with a query like, can you accept? The actual tailwind component is not absolutely reliably displayed on the 737 for various reasons. You can have the pilot non flying call it out from the FMC but there are caveats as to its accuracy. So the tower wind is the deciding factor. If you don't process the information and then fail to go-around when you miss the touchdown zone (which I see as just as big an issue as the tailwind) then this is what happens.