I know the question is old, but I had the same problem and I was able to find a solution.
The internal SWT browser uses the webkitgtk browser engine. Since you are using gentoo, I assume that you currently have net-libs / webkit-gtk: 3 installed, which is incompatible with SWT. But this is not a problem, because you can install compatible net-libs / webkit-gtk: 2 in a new slot. Just install it like this: emerge net-libs/webkit-gtk:2
After installing the package, the internal web browser works again (for me)
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