Yeah, a 40 amps is 4800 Watts, but that's output, not input. 110/120 volt household current circuits are a max of 30 amps, with 20 amps being typical, especially for older wiring. You plug something that draws 40 amps into a household electrical plug and it'll blow or trip a fuse immediately. For a 40 amp appliance you need a 240 volt circuit like a clothes dryer or oven or an air conditioner with those cоckeyed three spade plugs).
The "amp service" is the rating of electrical power available to your home. Most older homes have 60 amp service. Newer homes were updated to 100 or 150 amp service. The standard for most US homes today is 200 amp. You can find out what your service is by looking at the top breaker in your electrical box (or the Main Breaker), it should be stamped on that. But even if you have 200 amp service, you're not going to get 200 amps out of a single plug. You'll blow fuses or fry wiring if you try.
The "Input Current Cont is 2.0A, 4.5A, 10A" is what it draws, not what it outputs. The 200A jump start is achieved by a capacitor, not a direct draw from the generator or the household plug.
Since a 2000 Watt generator outputs 16.6 amps, yeah, it'll handle the 10 amp max draw of that charger with ease.