I have absolutely no idea what can be the problem. I did the pip installer (pip install pyttsx3) and re-installed the JetBrains PyCharm, but it still not working.
Start a pyCharm terminal window, then install 'pipenv' which is an improved pip replacement as follows:
pip install -u pipenv
Then use pipenv instead of pip as this will create it's own Pipfile and virtualenv. You can install pyttsx3 as follows:
pipenv install pyttsx3
This will create a Pipfile and a Pipfile.lock which pycharm should pickup and ensure it's using the correct python version and virtualenv environment. Otherwise check that your python interpreter is set correctly in "Run/Debug configurations". If it's not in that list then you can add a new python interpreter via the Preferences->Project->Project Interpreter option.