As long as you don't connect to shorepower (or generator) you are fine. The manual is unfortunately using vaguely written terms but to be clear there are two seperate grounds.
The DC grounding connector. There is a lug on the chasis of the inverter. This is for attaching a DC (not AC) grounding connector. This provides a backup protection in case the DC negative connection fails or the case becomes energized with DC
power through an internal fault. So in your DC diagram above you would have a third wire connecting the inverter. Ideally this goes to a seperate DC grounding bus with all other ground lug connections which is then connected to the primary DC negative bus which is connected to the DC negative on the
battery. However on smaller systems the DC grounding connector can be connected to the DC negative bus directly. It may seem weird that you have two DC connections (DC ground and DC negative) going the same place but much less AC ground the DC ground is a non
current carrying conductor. It is simply a
safety measure and would only carry
current in an
emergency. If the case became energized without a DC ground conductor if you touched it while say standing in
bilge water you would become the DC ground conductor.
The AC ground (third pin on NEMA outlets). The AC ground and neutral are bonded internally already in the inverter. There isn't anything else you need to do and in fact as the manual indicates you should NOT connect AC ground to DC ground/neg. You also if using AC
wiring not just the built in outlets should never connect AC ground to AC neutral anywhere on the boat. AC ground and neutral should only happen at one location and that is the source in this case the inverter.
Note due to #2 and the lack of neutral-ground switch
this inverter can NEVER be connected to shorepower or generator. It can't be used for other reasons as well (no ability to sync to the grid AC timing). Now from your described situation that likely isn't a problem just keep in mind in the future if you ever do upgrade to shorepower or
generator this inverter can not be connected to same circuits powered by shorepower or a generator. It could be used as an isolated inverter for circuits powered only by this inverter through battery. If all that seemed overly complex you can ignore it just keep in mind if someday you add shorepower or generator you need to revisit your design but you are fine until then.
Side note: I am fairly certain this inverter is not creating a floating neutral and that inside the inverter the AC neutral and AC ground (not DC ground) are connected. The wording in the manual is vague but it is saying the neutral and AC ground are not and should not be connected to DC ground. One way to verify is to use a multimeter and test for connectivity between the neutral and ground on the outlet. Likewise a connection between AC ground and DC negative or DC ground will show no connectivity.