@teots As said above, I think you're misinterpreting "if necessary" as "not needed", it's not the same thing.
There's good reason thermal paste has been needed since the dawn of PC building. No metal surface will be completely flat, there will always be small irregularities. Especially your image of the cooler base shows this clearly.
The job of the thermal paste is to smooth out these irregularities, getting into the small holes and ensuring a good heat transfer from the CPU to the cooler.
Playing a game is not a good stress test - games are too varied in CPU load, and most newer games are much more taxing on the GPU than the CPU. A better test is using a tool to load your CPU directly over a long time.
A great tool for this is Prime95, it calculates prime numbers and will max out all your CPU cores while running. If your system can run this for several hours without crashing or lowering the CPU speed because it reaches the heat limit, it means your cooling setup is working.
https://www.mersenne.org/download/