Since it is unlikely that anything smaller than a transport category aircraft will have an inertial system on board to feed data to an electronic HSI, there is a more likely explanation.
Most of the smaller aircraft will likely use a flux valve out in the wing, which is isolated from the plane's various electrical fields. This little marvel senses the change in its alignment with the earth's magnetic field, and creates an output signal that represents that relationship. Most of the time, this device is used to correct heading gyros on mechanical HSI's, but there is no reason that its data could not be passed through the necessary circuitry to drive an image of an HSI on the face of a tube or LCD screen. The latter screens are small, light, and produce very little heat, which makes them ideal for new or retrofits in small aircraft.
As mentioned above, you can feed these screens almost any info you like, such as approach charts, radar, TCAS, speed, altitude, text weather, engine data, etc. The possibilities are almost endless. When the virtual highway system comes along, a screen like this will display the image you will attempt to follow, much like a flight director shows the pitch and roll inputs necessary to let you take the place of the autopilot servos when you hand fly an aircraft.
Could an EHSI system contain an actual gyro? Sure. Like slicing a tomato, there are many ways to end up with the same result. Why not visit you local avionics shop and ask for an in-person explanation?