How to transfer an App from one ORG to another.

Currently, it's not possible. You have to republish App to that ORG. And you can do it by replacing code.

Just backup and delete this project then create a new project with the same name and replace the code.

Code replacement is quite easy. Just delete the App folder to the newly created project then copy the App folder from the existing project and paste it into the newly created project. 

Note: For classic app do the same for the Resource folder.

If you use any module then include it in your app tiapp.xml file. That's it.

Thanks