I am officially confused I could have sworn I saw some 5000 somewhere there and assumed 5kW inverter. It makes sense why they recommend a 200A fuse, an 8000W inverter at full load is 166A. You can pull up to a max of 100A per battery, two batteries in parallel can give you 200A.
That's where you need double cabling because one cable is rated for only 120A, double them, connect to a bus, put a 200A fuse and that's it. Or do it in any other way that satisfies the current requirements for the full load at 8000W.
Stay with the principle of current ratings and you won't be confused, the more current you draw, the bigger the fuse and cables, you can use the single cable on the 8000W inverter as long as you don't pull too much current you will be fine. So it's not about the inverter or batteries it's about the current you want to draw on any system.