Earlier quoted context omitted.
The Wikipedia page has a link to a thingie that says Duke Nukem 3D had clientside prediction. https://en.wikipedia.org/wiki/Client-side_prediction
I clicked your link and at first kind of brushed it off as dubious since the only linked source is a press article, but the article is an interview with Ken Silverman himself! So that's pretty credible. The source of the released game is available, so it should be possible to check, except that it's a huge mess (check out BUILD.C).[1] Seems weird that no-one has actually verified this when it could be the first game…
Because of the unique challenges, they did a lot of synchronized client-side simulation (based on minimal state transfer over the net).
... and apparently encountered a lot of the issues with doing that (no random anything!!!).