I understand what you are saying, but I feel that the word "daha" can be interpreted to mean both "more" and "still" in this case.
Examples of Daha meaning more in the sentences below.
"Selcen'nin senden daha çok gücü var". (Selcen has more power than you).
"O yuku kaldıramayacağını sandık ama bu adamın daha çok gücü var". (We thought he couldn't lift that weight, but this man has more power).
I was referring to a sentence in which daha can mean still rather than more. Examples: "Daha çok gençsin, değişeceksin". (You are still young, you will change). "Daha çok gücün var". (You have more power) OR (You still have a lot of power). Meaning you still have power renaining.
"Bu adamın daha çok gücü var" can also be interpreted to mean "This man has more power", as well as, "This man still has a lot of power remaining".
In fairness, the way the sentence is read out by the computer voice, there is partial stress on the word "çok" and full stress on "gücü", so it sounds like:
"Bu adamın daha çok gücu var"
When stressed this way, a native speaker would interpret it as:
"This man still has... (something)"
What does this man still have? - lots of power (the stressed words)
"This man still has lots of power"
If it were read out the way it should have been, there would be full stress on "daha" and partial stress on "çok" so it would sound as follows:
"Bu adamın daha çok gücü var"
This is interpreted as:
"This man has more of (something) [than...]"
The something he has more of is power, so it means:
"This man has more power [than...]"
I think it is very difficult for a non-native speaker to know this and the computer voice needs to be updated.
I hope that all makes sense.