> Tests on the other hand add maintenance cost: for example, once I (for balancement reasons) change the lifesteal coefficient, I'll have to reflect that change in tests.

Yes, and that's a good thing, because now you have to be aware of every ramification of your balance change.

Does the tutorial still play out the way you intended? Is that one boss fight still winnable with the intended strategy? Is that other boss still immune to life steal? In order to detect those problems you might have to play through your whole game from start to finish. But an automated test can tell you within seconds to minutes.

So an automated test allows you to go through every situation where the outcome is affected and confirm one by one that this is still the outcome you intended.

> Automatic tests are supposed to replace manual tests; but given I have to manually play my game anyway, isn't this duplication of work?

Automatic tests are not supposed to replace manual tests. They are supposed to augment them. While it can not replace the "how does it feel?" playtesting, it can save you a ton of work in regression testing (testing again and again if the things which used to work still work).