The author of the ParserComp entry “Race Against Time” has just announced that the game can now be played online here:
https://www.adrift.co/cgi/play.cgi?1794
No need to download anything. I played through it online, and except for a few layout differences, it plays very well online.
The announcement:
Race against Time available online - Competitions - The Interactive Fiction Community Forum (intfiction.org)