It's not really an architectural style. It's a mishmash of styles that are stuck together I order to look fancy to people who don't know better. People seem to like as many mismatched rooflines as possible, because that must fancier than a house with more restrained rooflines.
There are tons of houses like that where we are, and you just choose whether you want some stone veneer on part of it, or some faux-Victorian gingerbread trim, or some stick-on Tudor details made from foam or trimboard, or an oval second story window, or some black metal roofing over the porch. None of those things really match the house at all, but it doesn't seem to matter because they all get sold as fast as they get built.
I'm no architect, but I can tell you that no architect was probably involved in the design. The roof nubs at the highest points are a giveaway; no architect would make the roof planes meet in such an awkward way... Honestly though, for a house of that type, it's not too distasteful compared to many..
The windows that are boxed at the bottom with faux stone are making me grate my teeth.