A CPU is not an Application Specific Integrated Circuit. It is application agnostic.
Yes it is-- the circuit it implements is universal, meaning that it can emulate any other circuit. But it's built exactly like a mining asic is, mining asics just are more optimized for that task and don't waste space for parts that aren't needed.
The term ASIC is a comparison to early "integrated circuits"-- devices that had many semiconductor parts integrated into a single chip, but still exposed them to the outside world as generic parts. An application specific part builds the application (like "computer cpu") into it to achieve much higher levels of integration.