Board games have been printed on paper for something over 200 years. Many late 18th and 19th century games were printed on paper and glued to a fabric backing to reinforce them, and allow them to be folded and unfolded with a minimum of damage to the paper.
At Right: An Italian version of the "Game of Goose" (Il Gioco Dell'Oca Dilettevole) Pritned on paper and dating from the mid 18th century. Image scanned from Games & Puzzles by Caroline Goodfellow.
Four main techniques were used for printing commercial* games:
Engravings in wood, or copper: The majority of games published between 1770 and 1820 were printed from engravings. The design was cut directly into the end grain of a wooden plate or on a copper plate. This could produce fine, detailed lines, and colors could be added either by hand, to through the use of stencils.
Chemical Etching: A copper printing plate would be treated with an acid-resistant coating, into which the design was drawn. The plate was then treated with and acid which would etch the drawn lines into the plate. Because the design was not hand-etched or engraved directly into the metal this was a less expensive process as it did not require the skills of a metal engraver, and mistakes could be corrected simply by recoating the plate with the acid resistant coating.
Stipple Engraving: This was often used in conjuction with other printing methods, and used small dots to create shading or graduation in tones rather than cutting lines into the plates as with engraving.
Lithograph Printing: Lithography was invented in the end of the 18th century and evolved into modern offset printing. It involved printing from stone (hense the "litho" meaning stone) and is based on the concept that oil and water do not mix.
At left: Wallis's "Tour of Europe" published in 1794 as an engraving and then hand colored. It consists of 16 paper sections mounted on a linen backing. Image canned from Games & Puzzles by Caroline Goodfellow John Wallis, followed by his sons (John Jr, and Edward) was one of the most prolific British publishers of games from about 1775 to 1847.