Having the dumbbells facing each other is different from having them parallel to your shoulders. They do hit the chest, but not as directly:
- Your shoulders are in a more neutral and protected position, with minimal stress to the pec tendons. It's essentially safer and easier to go heavy with this form.
- It emphasizes your triceps, lats, and pecs in that order.
With sufficient weight and long enough sets, you should feel it in your chest. In fact, when you get closer to failure you'll feel it more in your chest as you struggle to keep the dumbbells from becoming a chest fly negative. I've used 75lbs for sets of 20 and definitely felt it both in the triceps and the chest.
Some of where you feel an exercise might just be where you are weakest at the time. If you feel it more in your lats at the moment, that's because your lats need to be made stronger to support reversing the dumbbells from the bottom position. As you progress or add other assistance work you may find you never feel it in your lats anymore.