From the documentation site you linked, Q4OS doesn't run inside Windows. The Q4OS installer runs inside Windows, and it stores the root filesystem for Q4OS as a file inside an existing Windows drive partition. I'm not personally aware of other Linux OS's that do either of these things, nor do I particularly desire a Linux OS that does either of these things. I can see it being useful if you want to keep your Windows installation fully intact. I imagine disk I/O performance takes a small hit.
Ubuntu used to have an option for that and the screen shot from the site looks quite a bit like the old Ubuntu installer.
I wouldn't be surprised if they forked that installer from Ubuntu at some point.
Can Q4OS installed that way access files from the Windows partition?
I have no idea, though I would lean "probably not" if I had to guess.
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