Most consumer grade inverters have a modified sine wave (MSW) output. Basically they are re-shaped square waves. Your videogame may be sensitive to MSW type output as is most life support/medical equipment. A true sine wave inverter costs much more but will not affect sensitive electronic devices. So it sounds to me that your problem lies with the type of AC signal that's being output from the inverter. I don't know what brand inverter the shop installed, but there are good quality MSW output inverters that perform more in line with true sine models in pale comparison to the bargain outlet store models. The high quality MSW inverter brands greatly lessen the chances of sensitive equipment experiencing problems.
Ground loops may also cause hum bars, especially in an automotive environment where devices are grounded at various locations throughout the chassis. This becomes a very critical issue when dealing with 2-way radio communications equipment.