4 new batteries and an inverter problems?

Inverter will not hold a charge like a battery does. Assuming the inverter has a charging function that is enabled AND the batteries are in good shape this should be a none issue

Edit typo

 

You need to know how many watts your game is running and if you had the laptop charging,how many watts does it use.
The wattage should be listed on each one.

 

For clarity & fix typo...

Inverter does not store energy like a battery would. It simply takes 12 volt DC energy from a source such as battery or alternator and converts to 110 volt AC.

Some inverters also charge batteries. If the batteries will not accept a charge due to being run down too low you sometimes can fake out the charger by putting a good battery in the series to provide a 12 volt source.

 

Depending on how efficient the inverter is and if the game is consuming max power, it should be about 35-45 amp draw on the batteries.
It’s possible they didn’t connect something right or didn’t tighten all battery connections.

 

What was the symptom that let you know you had 3 bad batteries for them to be replaced? If there is an underlying problem with the truck's charging system then it may affect your new batteries too

 

Most inverters of that size have a light gauge to indicate the AC out draw. If yours does, watch it when you are playing and see what the draw is. If you turn on your inverter by remote, you may have to put your phone on video mode and set it to watch the inverter for a minute or two, then watch the video to see the gauge.
Were you idling when this happened, or shut down?