Their energy saving part is to have the ability to shut down unused outlet to save from so-called "phantom" power draw.
Example: power outlet1 is the "master" outlet, where the built-in circuitry will monitor that outlet to see if the device is actively in-use or has been shut down (powered down). If powered down, the circuitry within that power bar will shut down the rest of the "slave" outlet ports to kill the power use completely. (until the master outlet port is being power up).
Again, this has nothing to do with surge suppression (like I said before: these 2 are mutually exclusive features).
Before EnergyStar tier-3 standards come into effect recently, most older (standby-capable) equipments would still consume between 3~12watts even when powered off. The idea of these so-called "energy-saving" power bars supposed to help cut down those "phantom" power draw to help save electricity.
With the new Tier-3 in effect, all EnergyStar appliances allow around 0.3~0.8watts(max?) of idle (aka "phantom") power draw only.
Lastly: these green energy-saving power bar does not work properly 1/2 the time, citing that unless you have something with high-power draw during normal operating conditions, and comes with less than 3watts (nominal) during shutdowns, many of these circuitry within the power bar failed to properly control the slave outlets because they cannot differentiate between a relatively efficient "master" load (e.g. LED based TV or PC monitor) and when they are actually powered off, causing all sorts of false operation (would not shut down the slave ports properly).
There was one of those energy-saving power bar that allows you to adjust the shutdown sensitivity of the "master" device, but I forgot what brand it is.
Q.