"Chassis" is the metal housing of the appliance. "Connected to chassis" literally means one of the incoming wires is electrically connected to the metal housing, and usually is implemented by one of the wires ending in a ring terminal which is screwed to a sheet metal panel somewhere.
As noted in your question, in the USA-style scheme, we regard earth ground and "neutral" as the "zero volts" reference. We have 120 volts between either of the mains lines and that neutral/ground reference, and 240 volts between the two mains lines.
You can see what would happen if a Euro appliance has one of its mains wires connected to the chassis (metal cabinet) and this were wired to one of the USA mains lines. Whereas made-for-USA appliances do have their metal cabinet connected to earth ground, if this Euro appliance has its metal cabinet connected to one of the mains lines, then we'll have 120 volt potential between the metal cabinets of the two appliances. A person touching the metal cabinet of the Euro appliance while also touching another appliance, or a sink, etc, will receive a shock.
On the other hand, if the Euro appliance is isolated so that neither of its mains wires connects to the chassis, then for use in the USA the chassis could be connected to earth ground and the appliance could be operated safely.
There's no need to disconnect the neutral at the breaker box. Unused conductors can be capped in any junction box where it's convenient to do so.