During the announcement, Samsung did say that there would be software updates coming to the Samsung Galaxy S III, S4, and Note II, which will expand Galaxy Gear compatibility to those devices, but the company has confirmed that it will eventually bring compatibility to non-Samsung smartphones. Apparently, one major point is Bluetooth 4.0 low-energy compatibility. Many manufacturers have built-in the capability for Bluetooth LE, but Samsung says the Gear works with the support in Android 4.3.
Of course, that leads to a question of why the Gear wouldn't work with the Nexus 4, Galaxy Nexus, or one of the Google Edition devices. The answer there is that there are some special programming interfaces built-into the Note 3 to allow for more advanced functionality between the Gear and Note 3 (we're assuming that refers to Samsung's Smart Relay feature.)
But, Samsung director of product marketing Ryan Bidan said that Samsung is "looking for additional devices to support it", and that support for more devices will come in time, but at first you will need a Galaxy Note 3.