The original implementation of CLONE_NEWUSER did actually convert users to vectors, or at least namespace-user tuples, which would have allowed unprivileged users to use the kernel UID mechanism for actual privilege separation. But that was dropped, I believe mostly because it was too much churn to the rest of the kernel and thus too risky. The current approach means that code that just thinks about root-namespace users continues to do the right thing.
The primary thing Chromium's sandbox seems to gets out of CLONE_NEWUSER is the ability to call chroot without shipping a setuid binary.
I stand (embarrassingly) corrected.
My concern is that you can clearly browse and save files, so there is something that has access. Maybe it's much more secure than I thought, but I tend to be really skeptical towards programs of such length being perfectly secure.
I believe the Chromium sandbox mostly applies to things like renderers, where you can just hand it a buffer and a bunch of inputs and it'll effectively contain things like HTML parser bugs or libpng buffer overflows. I'm not totally sure if browsing itself is sandboxed.