Q1K3 was developed for the 2021 edition of js13kGames, a JavaScript coding competition which has been running since 2012. The file size limit for all submissions is 13 kilobytes.
As noted by @stasisgame, that's smaller in size than the image included in this tweet:
While it can't be called an exact reproduction of the original, it manages to get the feel of Quake nailed down pretty well. There are two levels, five enemy types and three weapons – as well as music from Andy Lösch, dynamic lighting and decent AI. You can give it a spin here.
This year's js13kGames competition will commence on 13th August and end on 13th September.