The Spitfire documentary got me wondering if this feat of engineering was the point of difference in WWII? Or is there something more significant?

No. The Spitfire was good in many ways. It was fast, agile and in 1940 fighting over home turf. But it was very poorly armed until cannon were fitted in the "B Wing" MkVB and later. The Bf-109 was good in many ways... different ways to the Spitfire. However - the British had far more freedom to develop because global supply chains were still open in a way that was denied to Germany. There were very smart engineers working for Britain. Just like there were for Germany, for Japan, for the Soviet Union and for the USA. But the German ones operated under far tighter material constraints.

You can get a very good - and enormously detailed - description of a lot of this in Calum Douglas' "The Secret Horsepower Race - Western Front Fighter Engine Development". It is heavy going if like me you're not actually an internal combustion development engineer. But well worth the effort of sticking with it.