Result of today's experiments:
Doom on a NeXTcube turbo /w NeXTdimension runs in a small window, is slow and has no sound. The original Web browser is useless nowadays. ☹
But: It still works and it can connect to the LAN. 🙂
I tried it on spiegel.de won't work - log looks like there an incompatibility on the HTTP protocol. OmniWeb does download the HTML but shows a broken page.