Most European residential electric systems operate at 240v, versus 120v in the US, which means you can only backfeed a US outlet with half the power you could in a European outlet. That alone makes this system half as useful for US applications.
If one of these were made for the US market it would obviously be configured to work at the US mains voltage and frequency. (Europe is 50hz, US is 60).
Your home's power input is also 240 volts in the US, regardless of being split into two 120 volt rails at the breaker box. It would be trivial to hook up a 240 volt system if you really wanted to, albeit not through one of your regular 5-15/5-20 outlets. You'd have to do it via a dryer outlet or something.
Watts are watts. If the unit is capable of feeding 800 watts into your home's electrical system, the voltage is irrelevant provided it can supply sufficient amps. A normal US household circuit is 15 amps, so a hypothetical US version of this thing would have to supply ~6-2/3 amps at 120v rather than ~3-1/3 amps at 240v. No big deal. It's not even close to maxing out a single residential circuit on either continent.
Just want to post a pic of a 20a 220v US outlet for those who don't know about it.
It fits in a standard box, so you don't have to use a dryer plug if someone wanted to feed power back in through a outlet. (Of course with a device designed to feed in safely.)
Your home’s power input is also 240 volts in the US
It's not actually 230V in Europe, it's 400V. Between each pair of the three phases, that is, between phase and neutral there's 230V. (If there's a neutral and you don't create it locally, different topic).
...but I'd actually have different doubts about using the whole thing in the US: Your plugs. Schukos aren't meant for the purpose and only code for up to 800W when used to backfeed. That's almost 1/5th of their 1 hour continuous rating. With those flimsy tinfoil plugs you have you're going to need special outlets, or hard-wire them.