Parshape isn't as expressive as the CSS float model, because the entire shape of the paragraph has to be specified up front. CSS floats, though, effectively change the shape of the block as the block is laid out.
I'd argue it is just different. CSS floats really only deal with square shapes, still. (I could be behind on this point, not something I've cared to do in... well, ever. :( )
Quickly googling for the example from the TeX-book of the text in a circle doesn't give anything similar for html.
Rectangle vs circle isn't the point of this thread, as I understand it. It’s that the calculated width of text determines the width of a float when the float has no specified width. Here is a fiddle demonstrating what I understood people were talking about regarding floats, although it is a different thing than the other jsfiddle in this thread is showing: https://jsfiddle.net/1wj3efkm/
The width of the float not being fixed seems like a massive goal post shift. Unnecessarily so, honestly.
That said, this problem doesn't seem that much harder, honestly. Each float has a max size. They are only smaller if they had less text.
And see the example in the TeX-book. Basically a circular cutout for text aligned on a circle. Both parts fully hyphenated to fill the outline. I'm on my phone, but will try and find an example, if it would help.
It's true that there's no feature that directly corresponds to parshape. (This is what the ill-fated CSS Regions spec was for; the problem with it is that it was far too expressive to the point of becoming near-unimplementable.)
However, I believe you can simulate parshape by just stacking line-sized floats on top of one another and using clear to stack them vertically. This should give you just as much expressivity as parshape.
I think the advantage TeX has here is only over HTML. Specifically, that it is a full programming language. Well, mostly full. Adding in JavaScript and I don't know how the web couldn't do these things. Some of the abstractions will make it harder, of course. But some will make it easier, too.
