Electronic

I had one of those plug in inverters. 300 watt. The thing struggled to power a laptop.

 

Can you look on your TV and your game system where the power cord is connected to the TV/game system? Tell me what it says beside the voltage. It will says something about amps (A) or watts (W). Multiply the voltage times the amps and that equals watts. If you are lucky it will tell you the watts consumed by the device.

On your inverter it will typically state it's output in watts with a "peak" and a "continuous" rating. I would first power up your game system and let it boot and then stabilize then turn on the TV, if possible. SOME devices pull about twice their rated-power for the first second then drop down to normal. If the number you posted are accurate they should work with your inverter.

 

The game system should build up its capacitor as soon as plugged in that is why they still have a small draw when powered down but plugged in same with TV... So I would alternate the plugging in of devices more so then the powering on... Now devices without a control circuit or AC to DC converter aka power supply will peak when powered on a refrigerator or drill for instance of course a drill would peak Everytime you pull the trigger

 

You should be OK with a 300 watt inverter as long as you can idle the truck otherwise batteries probably won't keep a good enough charge

 

A 400 would be better but won't get around the need to idle as it will still draw the same power from the batteries
I am assuming you don't have an APU either honestly as soon as you get enough exp if you don't have it already find a new company no APU no inverter not allowed to idle... That company doesn't give 2 shots about its drivers just my opinion

 

You won't be getting 300w from a plug in inverter. It's more like 120-150