The Essential Phone uses a gyro-based EIS for images according to a response that was given to a user from the official Essential account on Twitter. When asked about how the Essential Phone handles image stabilization, Essential, or whoever runs its Twitter account, replied saying that it was a gyro-based electronic image stabilization system that was being used. Though not everything with this system will be entirely the same, EIS is the same kind of image stabilization technology that Google uses in the Pixel and Pixel XL, two phones which were ranked as the best smartphone cameras to date until the HTC U11 came along. This doesn't mean that the Essential Phone will have the same kind of success with the camera, but the fact that it's using the same kind of technology to stabilize images and video during use of the camera seems like a pretty big deal.
According to some of the other users commenting on this question, the Essential Phone website doesn't list EIS as a notable specification for the device, and if you go to the Essential Phone website you'll notice that any mention of image stabilization in general is completely absent. Under the specs category it does list off the quality of the camera, and other traits are listed such as phase detection autofocus and image fusion technology, but there's no mention anywhere of Electronic Image Stabilization.
Though some would argue that OIS is much better than EIS, having either of them is better than having neither of them, and usually companies list when things like OIS and EIS are present. Without getting into the technical details of EIS, it basically just helps cut down on the hand shake or camera shake that one might get with too much movement during shooting, so it's definitely a good thing that the Essential Phone is packing such tech, though how well it serves its purpose remains to be seen since the phone hasn't been made available to consumers, which means no one has been able to really test how well the camera works in any capacity let alone just for how stabilized the pictures and videos look. Interestingly enough, although the Essential Phone hasn't started shipping to consumers, it was recently spotted in use by someone who was riding public transportation, so perhaps the arrival of this device is just around the corner.