If the basic GCT requires say 49.5 watts which is the combination of all the componants such as the LCD, CPU and mainboard consume which is usually rated in amps, the power supply must supply at least that amount of flow (AMPS). the supply of 19 volts must be supplied but at the same time there must enough flow to supply the computer with enough flow. Now watt's is a measure of electical flow at a given voltage which is calculated by multipling the voltage times the amps rating of the given source of power to determine the total watts that are required. The PSU that you described is a 79.8 watt supply which the company that makes the PSU will market as a 80 watt supply, That supply should work fine on a GCT or even most gateway Solo notebooks.
Suppling more watts than a device requires will not harm it, suppling more or too little voltage to a device can cause malfunction, non-operation or even let the magical smoke out... :) Suppling too little wattage in such as a under rated power supply puts a load on the given power supply which can cause it to over heat, melt and even perhaps catch on fire; When the device starts pulling more much load or current than the power supply can provide then the voltage will drop and damage may occur to device due to undervoltage.
A flashlight with batteries is a good example... the batteries are the power supply, when the batterys lose their "push" or power, it because they can no longer provide the necessary wattage to drive the device which is the light bulb, as the wattage "push" in the batteries die, not as many volts is supplied and the light dims as less voltage is supplied. The newer "super" AAA and AA batterys which last longer are just better suppliers of higher wattage which allows the battery to supply the 1.5 volts for a longer time.