It's sort of a "queen anne meets the country cousin" style. This is actually a poorly conceived furniture design; it looks like it's trying awfully hard to be a formal "Queen Anne" set (the turning of the legs, the dark mahogany etc), but those horizontal slats on the chairs are pure country.

This is not casual in the least ~ it's the chair backs that are giving you the illusion of being a country set.

It's definitely formal. Queen Anne is far from country. If the rest of your home is more casual, this would look out of place.

I think it is formal looking but I don't know your life style. What makes it look formal to me is the wood color and the china cabinet which I don't like at all. I had a mahogany set for years that cost $6000 and I finally sold it for a more practical, simpler table and chairs that I am much happier with. If you like it and it's going to be in a formal dining room and not used often,, then buy it. If you aren't sure if you like it enough though, then you probably don't. Wait til you fall in love and are sure. A leaf is always a nice option too.