Speaker-dependent Voice Recognition
Is it possible to use Maix_Speech_Recognition for speaker-dependent voice recognition on Arduino Uno compatible boards?

No. It's not.

What part of Maix_Speech_Recognition should I modify to make it work on Arduino Uno compatible boards?

Don't even think about it. The UNO cannot do anything even remotely like speech recognition of any form without adding extra specific speech recognition hardware.
Just get a K210 board - they're cheap enough.