The big breakthroughs were the ability to simulate hardware for larger circuits at higher frequencies realistically to determine how to make those circuits stable rather than to get them to oscillate wildly at the frequencies they operate at. Once you develop a bit of appreciation for what is required to make a 100 gates work reliably at 10 MHz or so you can begin to understand the black magic required to make billions of transistors work reliably at frequencies in the GHz.
So the skill is not at all related to puzzle games, but it is a puzzle and the tools and knowledge required were usually hard won. At those frequencies and part sizes anything is an antenna, there is no such thing as a proper isolator, coils, resistors and capacitors all over the place even if you did not design them into the circuit (parasitics).
If this sort of stuff interests you I highly recommend the 'Spice' tutorials, and/or to get an oscilloscope and some analog parts to play with.