It would have been an electrical (or possibly mechanical if they could make it light enough) analogue computer. Analogue fire control computers were common on naval ships from WW1 onwards, and used in bomb sights and anti-aircraft guns in WW2. I presume that it would just be a moderately complex negative feedback system.
Mind you, the pictures make it look like it wouldn't really have been a useful military plane. Too small to carry any significant load, guns, or fuel. It was designed as a racer, not a military plane, and while companies like Supermarine could apply lessons from racing to mass-produced military machines, they still had to design the military machines from scratch and not just do quick adaptations to existing designs. The Spitfire, for example, has its origins in a 1931 design, and had two substantial re-designs before finally entering service in 1938. Even if the Germans get their hands on this unfinished prototype in mid 1940 when France falls, there's not a chance that they'd get anything related to it into production until they're already getting their heads kicked in by the Red Army and RAF Bomber Command.