Comparing to Google Docs isn't the point. (Although it would be good if it compares well.) This is really aimed at people who have already integrated Dropbox into their workflow -- enterprise customers, mostly.
Unless notes sits on your OS and doesn't require you to boot up your browser and log into Dropbox then, yes they are competing with google docs. I work with an organization that has dropbox set up for around 140 employees and most of them don't use it beyond the desktop integration, why would they?
In my experience, the most common way to share files is by creating sharable links at dropbox.com. In fact I think that might be the ONLY way that I'm aware of.
You can share entire directories, like a network drive.
True. I did find it odd how closely the screenshot resembles Google Docs though. Granted there's not a lot of UI there to compare against, but given that it seems to be the only hint at what Notes actually is, I expected a bit more.
Yep, they can compete on convenience in this regard. I can't imagine they'll work to introduce a full Microsoft Office competitor like Google has done with Drive, but if it works fluidly with the seemingly ubiquitous Dropbox client and web browsers I could see it succeeding.
Didn't Dropbox partner with Microsoft to offer Office Web app capabilities?