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Inkscape cannot automatically trace a photo, in such a way that it needs no further work, before sending to the cutter. Although I think someone could be successful, if they wanted to create a trace engine for such a purpose.
Anyway, I'm not so sure that's what has happened with your sample images. It looks to me like someone must have tweaked the vector quite a lot. The reason I think that is because the vector image does not look like a faithful reproduction of the photo. Specifically, note where the pylons of the wooden deck/wharf/boardwalk meet the water, there appears to be ripples in the water. But the photo does not have any such ripples, or anything that might cause those features.
And also, look at the surface of boardwalk on the vector image. It would appear to be darker along the edges, and lighter along the middle area. But in the photo, I don't see anything like that. The deck looks fairly much the same, whether you look at the edge or the middle. And I could make similar comments about the horizon and reflection of the mountains on the water.
Somewhere I've seen examples where Illustrator's trace can almost perfectly reproduce a photo. But perhaps the version you tested does not have that. Inkscape's Trace Bitmap should be able to get you a good start at it, though. Especially by tweaking the various options in the dialog. You'll just have to do a good deal of trial and error, with the settings, and still probably a good deal of node editing, to create the effect you want.
Also, there are other trace engines, which work differently than Trace Bitmap, which might get you closer to what you want, in one go. But you'll still need to do a lot of trial and error, until you learn how the various settings affect the outcome. Here's one other tracer that I know about:
http://www.roitsystems.com/cgi-bin/autotrace/tracer.pl And there's another vector program, which I think can trace....I wanna say Vector Magic, but I'm not positive about that.