Worn patch in Floating Floor

We have made the mistake of using a computer chair with wheels directly on a new Floating Floor in the house we were renting. Now the floor has a patch where it has become worn. It is probably a metre square that ruined area. We have have a quote from the company who installed the floor and the quote was $550 because apparently they have to resand and polish half of the room. Total room is 4 meters by 4 meters.

I am just wondering if this quote is about right. And if this is what has to be done, resanding and polishing or is there no polish that you can just put on it to bring the colour back?

It depends on what the floor was finished with. The trend for "quick" finishes has made poly-based finishes more popular and they're normally quite hard-wearing but are beggars to repair.

Assuming poly, and that a good job is done, in my opinion that's a reasonable estimate.

If 'tis an oil-based finish, eg. tung oil, then only a light sand and recoat is needed, but it sounds like you're stuck with a poly...