How to run the cumulocity widget in my local machine

You can check the command output, as it shows where it is proxying to:

Proxying requests to remote instance http://demos.cumulocity.com

Please check if you follow the documentation and use e.g.

c8ycli serve -u https://mytenant.eu-latest.cumulocity.com

https://cumulocity.com/guides/web/development-tools/#c8y-cli