I have previously made much of A Journey Through Europe, published in 1759, and the first boardgame in the English language to which we can ascribe an individual designer; I called it "the first designed game," and Rob Rossney quite rightly pointed out that the card game of Cribbage was designed sometime around 1630 by Sir John Suckling. But at least until now, Journey was the first designed boardgame of which I know.
However, BibliOdyssey brings us word of a game published in 1680 by Giovanni Pare, in Italian, and designed by Don Casimir Freschot, a Benedictine monk who was also a notable historian in his day. BibliOdyssey claims that the image above is "from a map game" he conceived. However, the BibliOdyssey article (and the gallery site, linked above, that is selling this map) also says, "While in Venice he [i.e., Freschot] also composed a goose game to facilitate 'the teaching of geography to the young Venetian nobility.'"
The problem with this description is that The Game of Goose is a folk game, dating back to the 17th century and possibly before, with well known mechanics: it is a track game, or a "race game" in Parlett's parlance. Players advance tokens along the track according to the throw of dice (or rotation of teetotums), and some spaces cause an additional roll, lose you a turn, or advance or retard you some number of spaces, according to mechanics with which we are all no doubt familiar. Jeffreys's Journey is, in fact, a Goose variant, differentiated mainly by the fact that it is played on a map of Europe, and that the text associated with each space provides some mildly educational information about the location portrayed, as well as the usual game-specific direction.
It is entirely feasible that Brother Freschot created a Goose-like game to teach geography; after all, Jefferys did likewise. It is also entirely feasible that the image above derives from some sort of game; the squareness of the images, and Altea's description of "153 smaller maps of other areas" suggests tiles used in some sort of gameplay. Yet I note that there is nothing track-like about these map images, and if they were arranged in a track-like manner, we have no evidence of that, and certainly we see no text suggesting the game importance of the image. Consequently, we have to assume that either a) these maps are from some other, non-game, project of the good Benedictine, and that his "goose game" has yet to be discovered; or b) these maps are indeed from his game, but the game was not, in fact, a "goose game". Or possibly c) The map images are designed to be arranged in the form of a track, but the rules by which they are used to create a game are still to be discovered.
Still, this is all very interesting, I'd love to know more -- and if readers are aware of any other games ascribed to individual creators that date to the 17th century or before, I'd be delighted to hear of it.