After reading the following question on stackoverflow.com: http://stackoverflow.com/questions/42585255/how-to-run-typescript-not-angularjs-unit-tests-with-jasmine-and-webpack
I figured, this shouldn't be to hard. And well, it kinda was.
But it's working, so that's why I'm sharing this.
The key to this was this comment: codymikol/karma-webpack#188 (comment)
That is why karma couldn't see the *.ts files
To run the app with node:
npm start
To run the unittests using karma -> jasmine
npm test