The Inverter type generators is just the method the generator uses to develop its 120VAC output.
Do not confuse this technology with stand alone INVERTERs you will need to operate your Trailer Home entertainment items like the HDTV, DVDs, and other sensitive electronics when camping off the power grid.
In my setup I have a 600WATT PSW Inverter direct connected to my 255AH battery bank to operate my sensitive electronics when camping off the power grid. The 2KW Honda Generator is only used to re-charge my batteries in a short three hour generator run time when allowed to run my generator as most places we go to only allows us to use our generator a few hours each day. I have beefed up my trailer to smart-mode converter/charger technology which will re-charge my battery bank in a short three hour time period each day. I have my battery bank large enough to run all the 120VAC items we want to run from the 600WATT Inverter and the 12VDC items directly from the trailer battery system and then at 8AM each morning we are usually allowed to run our Generator with the trailer 30AMP shore power cable directly connected to the generator 120VAC receptacle using a RV30A-15A "DOGBONE" type 18-inch long adapter (WALMART). Once the battery get re-charged back up to its 90% charge state then we can do all of this all over again for the next day/night camping experience off the power grid.
Your generator listed that you found for sale will most likely be a LOUD contractor type generator since it is not an INVERTER TYPE and may be a problem running around your neighbor campers. Other than that it should work just fine with your trailer shore power cable connected directly to it to re-charge your battery bank as connected above.
The problem is that most places you go camping at may NOT allow the use of generators during the times you want to run the generator so you need to develop a plan to run everything from your batteries during most of the camp ground visit and only run the generator when allowed to do so which here on the east side of the US is usually only from 8AM-10AM in the mornings and then again from 4:30PM-7:30PM in the early evenings at the regular camp grounds. Alot of Natlional forest have the same rules in place but alot also allow the use of generators from 8AM to 8PM. I have never been at a public place that allows them to run 24 hours a day. Maybe a NASCAR event... Generator restrictions are different I think the farther West you go in the US probably because of the larger wide open spaces you find.
If the places you are going to allows the use of generators 24/7 and the folks around you don't mind the noise get the cheapest loudest generator you can find I guess... Didn't work out that way for me...
Does any of this make any sense haha...