I saw the package.json as there is no command like npm run start or no docker file present. Is there any other way to run this app on localhost?
Generally, a single app is not runnable without the NC core. You will need an installed test instance of the NC server in order to run/debug any app within it.
In your case, I suggest to have a look at the development environment provided by Julius Haertl. There is some documentation on how to setup a development instance using docker on the local machine.
Having done that, you should be able to develop according to your needs (be it backend step debugging or frontend Vue development).
I hope this helps to get you started. Feel free to ask further.