Angular Template Webpack is broken

I am trying to set up a project using the new Angular Template inside ASP.NET Core. However, when I try to run the Development or Production tasks in Task Runner, they always terminate with an error in @ngtools/webpack/src/plugin.js at line 8. 

The error is as follows:

const { __NGTOOLS_PRIVATE_API_2 } = require('@angular/compiler-cli');
      ^
SyntaxError: Unexpected token {
    at exports.runInThisContext (vm.js:53:16)
    at Module._compile (module.js:373:25)
    at Object.Module._extensions..js (module.js:404:10)
    at Module.load (module.js:343:32)
    at Function.Module._load (module.js:300:12)
    at Module.require (module.js:353:17)
    at require (internal/module.js:12:17)
    at Object.<anonymous> (C:\<my path>\AngularTest\node_modules\@ngtools\webpack\src\index.js:30:10)
    at Module._compile (module.js:397:26)
    at Object.Module._extensions..js (module.js:404:10)

What do I need to do to fix this? I suspect it is why I am getting a lot of other errors as I try to add new components.