What does "get fried" mean or look like? If it's complaining of an open ground, you may have a problem with the neutral-ground bond at the generator (which should be a pretty simple fix) or a problem with the automatic transfer switch, if you have one. If it's instead that the MOVs are getting worn out, the power waveform is probably not clean with the generator unloaded or very nearly unloaded, or the generator voltage is a bit high unloaded (which may mean it needs adjustment). Turning on additional devices would help in that case. (Typically, any voltage spikes are low-power noise.)
The Onan should put out reasonably clean power. The surge protector probably is quite unnecessary, particularly as it's fairly likely that the console and TV have multi-standard power supplies that accept most any AC power from 100V to 240V without complaint. You aren't going to have any of the typical sources of power surges between the generator and the rest of the RV, such as lightning strikes or industrial equipment on the same supply grid starting or stopping.
For running the game console while traveling, a modest inverter would seem to me to be a very good investment. It wouldn't take too many hours of use before it pays for itself over the gas required by the generator (about half a gallon an hour, more or less). The engine alternator via the battery isolator will be able to keep up with the power demands of the console and TV while driving so the house battery will not get discharged (but it probably won't charge as quickly from the engine).