Welcome Angular 2 rc.3!
I use project.json from 5 Min Quickstart to configure my project, but when i run npm install i get follow error:
Angular2 RC3 brings back the new router. But the Tutorial continues to mention router-deprecated. Check out the Developer guide which has documentation on the latest Router: https://angular.io/docs/ts/latest/guide/router.html
As mentioned in the comments, you can give it a try using
"@angular/router": "3.0.0-alpha.7"