JF Ptak Science Books Quick Post
--"Whoever first arrives here is to take the title of Astronomer Royal'"--end point of the game The Pleasures of Astronomy
I'm not sure how early the earliest board game featuring a scientific game might be, but I do know that this one--Science in Sport, or the Pleasures of Astronomy; A New & Instructive Pastime. Revised & approved by Mrs. Bryan; Blackheath--seems to be very advanced for its age. Made in 1804 by John Wallis on London, the game such as it is isn't very "game-y"--the gaming aspect of it isn't very interesting or involved--mostly the mostly-representative aspect so the game is to just expose the young players to select aspects of the history of astronomy. As a pedagogical tool, the game probably works pretty nicely.
The game board, or the course of the game, is relatively standard, though the subject matter is not. The object was to arrive at Flamsteed House1, and by the course of victory the young player would become acquainted with elements of morals, ethics, natural philosophy (although Wallis did in fact produce a very similar game for that topic alone) plus of course some basics of astronomy.
1. "Flamsteed House, the original Observatory building at Greenwich, was designed by Sir Christopher Wren and Robert Hooke and built in 1675-76." See here for more information.