Google has been increasingly transitioning new features in Android to a more closed model. Whether you're talking about music playback, search, or even the dialer, Google's updated apps have features not included in the Android Open Source Project. The developers of OmniROM are looking to make the handy features of the new Google Dialer available without the proprietary bits, so they're working on an integrated phone number directory without Google.
Of all the announced new features of the Nexus 5 and Android 4.4/KitKat, one of the cooler ones was a new dialer colloquially known as the "KitKat dialer." It features a revamped UI and includes the ability to search for businesses, contacts, etc. right from inside the dialer. It also features Internet-based caller ID. The name "KitKat dialer," however, is not entirely accurate.
Google Dialer (its official name) is not technically part of KitKat because it is not included in AOSP.