QA experts do not use the word 'test automation'. They rather call it automation checks as they feel testing cannot be automated, but checking can be totally automated. Humans have the ability to do things, observe things, and examine things that computers cannot. Our humanity as testers plays a big role in identifying defects while testing. A computer cannot experience or cannot express emotions.

A computer cannot 'determine if the game is fun or not?' ..... 'if an app has good user experience or a pleasant interface'..... Or to 'take decisions using investigative/inquiring etc. Automated test can only find defects that you already thought of or predicted might happen.

You may ask if the test automation can run the same test more quickly, more accurately and with same consistency every time, is it not a better than a human tester?

No! Because running a test quickly with more precision and consistency does not produce better software but it would definitely reduce the time required to complete testing. Test Automation may be one of the most helpful weapon in tester's checklist. It has its own place in the checklist/inventory. The weapon is useless without its wielder. Automated tests require scripts to be written and maintained, this in turn requires a HUMAN.