7 Kw equals 58 amps of AC power at 120 volts. The circuits you run to your gaming machines will be 15 or 20 amps per group of games. I'll bet you can plug at least a half dozen game consoles into a single 20 amp circuit without any problems.
RV generators run for hours at a time when they're parked in a campground, often running high draw air conditioners along with the rest of the RV's loads. So you shouldn't have any problem running your gaming machines.
Take note of what kind of fuel the built in generator uses. The generator can be gas, diesel or propane. Gas and diesel draw from the vehicle's tank, with a built-in shutoff if the tank drops below about 1/4 full. This is so they can't strand you without a way to drive the RV to a filling station.
Propane generators draw fuel from a propane tank, the same one that feeds the propane stove, water heater and gas furnace. They create the cleanest exhaust, but you have to refill the propane tank on a regular basis.
Figure on using between 1/2 and 1 gallon per hour of fuel, with diesel being the most efficient, gasoline being in the middle and propane coming up last (using the most fuel per HP).
As far as the exhaust goes, most generators just exhaust them down low adjacent to the wall of the RV. This can create carbon monoxide problems inside if the wind is blowing just right, so CO detectors inside the van to alert to CO buildup are a must.
You can minimize exhaust buildup by extending the generator's tailpipe up and beyond the roofline, so convection can carry the hot exhaust gasses up and away. You can permanently plumb the exhaust this way when you do the remodeling, or purchase an aftermarket exhaust stack called a Genturi that clamps onto the generator tailpipe and the RV's wall.
